diff --git a/examples/goalOrientedAFEM.m b/examples/goalOrientedAFEM.m
index a07806216b2b6a115b00a751585e3797c48ba33d..59fd93992125b6d2106dfb0a5b7180b4a1937fb8 100644
--- a/examples/goalOrientedAFEM.m
+++ b/examples/goalOrientedAFEM.m
@@ -3,9 +3,12 @@
% ******************************************************************************
%% paramters
-nDofsMax = 1e4;
+nDofsMax = 1e5;
theta = 0.5;
-pmax = 3;
+pmax = 4;
+
+step = 1;
+while step< 3
%% initialization for every polynomial degree
[nElem, nDofs, goalErrEst] = deal(zeros(pmax, 1000));
@@ -57,15 +60,27 @@ for p = 1:pmax
zeta2 = estimate(blf, lfG, z);
nDofs(p,ell) = getDofs(fes).nDofs;
nElem(p,ell) = mesh.nElements;
- goalErrEst(p,ell) = sqrt(sum(eta2)*sum(zeta2));
- printLogMessage('number of dofs: %d, estimator: %.2e', nDofs(p,ell), goalErrEst(p,ell));
+ %% goal estimator
+ goalErrEstGOAFEM(p,ell) = sqrt(sum(eta2)*sum(zeta2));
+ switch step
+ case 1
+ printLogMessage('GOAFEM: number of dofs: %d, estimator: %.2e', nDofs(p,ell), goalErrEstGOAFEM(p,ell));
+ case 2
+ printLogMessage('AFEM: number of dofs: %d, estimator: %.2e', nDofs(p,ell), goalErrEstGOAFEM(p,ell));
+ end
%% stoping criterion
meshSufficientlyFine = (nDofs(p,ell) > nDofsMax);
%% refine mesh
if ~meshSufficientlyFine
- marked = markGoafemMS(eta2, zeta2, theta);
+ %% switch here
+ switch step
+ case 1
+ marked = markGoafemMS(eta2, zeta2, theta);
+ case 2
+ marked = markDoerflerSorting(eta2, theta);
+ end
mesh.refineLocally(marked, 'NVB');
v.setData(prolongate(P, v));
w.setData(prolongate(P, w));
@@ -75,16 +90,25 @@ end
%% plot convergence rates
pmax = size(nDofs, 1);
-figure()
-for p = 1:pmax
+
+switch step
+ case 1
+ figure()
+ for p = 1:pmax
+ idx = find(nDofs(p,:) > 0);
+ loglog(nDofs(p,idx), goalErrEstGOAFEM(p,idx), '-o', 'LineWidth', 2, 'DisplayName', ['GOAFEM p=',num2str(p)]);
+ grid on
+ hold on
+ end
+ case 2
+ for p = 1:pmax
idx = find(nDofs(p,:) > 0);
- loglog(nDofs(p,idx), goalErrEst(p,idx), '-o', 'LineWidth', 2, 'DisplayName', ['p=',num2str(p)]);
- hold on
+ loglog(nDofs(p,idx), goalErrEstGOAFEM(p,idx), '--', 'LineWidth', 2, 'DisplayName', ['AFEM p=',num2str(p)]);
+ end
end
-for p = unique([1,pmax])
- x = nDofs(p,idx) / nDofs(p,1);
- loglog(nDofs(p,1)*x, goalErrEst(p,1)*x.^(-p), '--', 'LineWidth', 2, 'Color', 'k', 'DisplayName', ['\alpha = ', num2str(p)])
+step = step +1;
end
+
legend
xlabel('number of dofs')
ylabel('goal error estimator')
diff --git a/experiments/Neumann_exact.m b/experiments/Neumann_exact.m
new file mode 100644
index 0000000000000000000000000000000000000000..ef27907dd073a74b08b15ce4e41c77e867452691
--- /dev/null
+++ b/experiments/Neumann_exact.m
@@ -0,0 +1,189 @@
+% ******************************************************************************
+% Adaptive FEM algorithm for a nonsymmetric problem on the L-shaped domain
+% using the Zarantonello iteration from Section 6.1 in [Brunner, Heid,
+% Innerberger, Miraçi, Praetorius, Streitberger, 2022]
+% ******************************************************************************
+clear all; close all;
+%% parameters
+nDofsMax = 5e1;%1e2;
+pmax = 1;
+theta = 0.5;
+lamalg = 1e-1;
+delta = 0.5;
+
+%% initialization for every polynomial degree
+for p = 1:1:pmax
+ %% setup geometry & spaces
+ % leveldata = LevelData('results');
+% leveldata.problem = 'neumann_exact';
+% leveldata.domain = 'Lshape';
+ % printLogMessage('*** p = %d (of %d) ***', p, pmax)
+ % leveldata.identifier = ['p', num2str(p)];
+ mesh = Mesh.loadFromGeometry('Lshape');
+ mesh.refineUniform(1);
+ fes = FeSpace(mesh, HigherOrderH1Fe(p), 'dirichlet', 1, 'neumann', 2);
+ u = FeFunction(fes);
+ u.setData(0);
+ uZaraOld = FeFunction(fes);
+ uExact = FeFunction(fes);
+ ncFes = FeSpace(mesh, LowestOrderL2Fe());
+ w = FeFunction(ncFes);
+ Q = Prolongation.chooseFor(ncFes);
+
+ %% set problem data for -\Delta u = 0 on L-shaped
+ blf = BilinearForm();
+ lf = LinearForm();
+
+ blf.a = Constant(mesh, 1);
+ blf.qra = QuadratureRule.ofOrder(max(2*p-2, 1));
+
+ %lfF.f = MeshFunction(mesh, @(x) modifiedRightHandSide(x));
+ lf.f = MeshFunction(mesh, @(x) 0);
+ lf.neumann = MeshFunction(mesh, @(x) exactSolutionNeumannData(x));
+ lf.fvec = Constant(mesh, [0; 0]);
+ lf.qrf = QuadratureRule.ofOrder(2*p);
+ lf.qrfvec = QuadratureRule.ofOrder(2*p);
+ lf.qrNeumann = QuadratureRule.ofOrder(2*p, '1D');
+
+ %% set up solver and operator for nested iteration
+ [solver, P] = IterativeSolver.choose(fes, blf, 'multigrid', 'lowOrderVcycle');
+ solver.tol = 1e-8;
+ solver.maxIter = 100;
+
+ %% adaptive loop
+ ell = 0;
+ work = 0;
+ time = 0;
+ meshSufficientlyFine = false;
+ while ~meshSufficientlyFine
+ %% setup
+ ell = ell + 1;
+
+ tic;
+ [A, F] = assembleAll(blf, lf, fes);
+
+ solver.setupSystemMatrix(A);
+ freeDofs = getFreeDofs(fes);
+ solver.setupRhs(F, u.data(freeDofs)');
+ uEllExact = A \ F;
+ nDofs = getDofs(fes).nDofs;
+ nFreeDofs = size(freeDofs, 1);
+
+ jPrimal = 0;
+ jContractionPrimal = 0;
+ primalSolverIsConverged = false;
+ while ~primalSolverIsConverged
+ work = work + nFreeDofs;
+ solver.step();
+ jIncrementNormPrimal = energyNorm(A, u.data(freeDofs)' - solver.x);
+
+ u.setFreeData(solver.x);
+ eta2 = estimate(blf, lf, u);
+ estimator = sqrt(sum(eta2));
+
+ primalSolverIsConverged = jIncrementNormPrimal < lamalg*estimator;
+ end
+
+ uExact.setData(nodalInterpolation(MeshFunction(mesh, @exactSolution), fes));
+ jPrimal = jPrimal + solver.iterationCount;
+
+ deltaU = u.data - uExact.data;
+ h1Error = energyNorm(A, deltaU(freeDofs)');
+
+ %% stoping criterion
+ meshSufficientlyFine = (nDofs > nDofsMax);
+
+ %% refine mesh
+ if ~meshSufficientlyFine
+ marked = markDoerflerBinning(eta2, theta);
+ mesh.refineLocally(marked, 'NVB');
+ u.setData(prolongate(P, u));
+ end
+ time = time + toc;
+ relTime = time / nFreeDofs;
+ % leveldata.append( ...
+ % 'nDofs', uint32(nFreeDofs), ...
+ % 'nElems', uint32(mesh.nElements),...
+ % 'error', h1Error, ...
+ % 'estimator', estimator, ...
+ % 'time_cumulative', time,...
+ % 'relative_time', relTime, ...
+ % 'work', work ...
+ % );
+ % leveldata.printLevel();
+ end
+ if nDofs > 1e6
+ leveldata.saveToTable();
+ end
+ %leveldata.plot('nDofs');
+end
+
+
+%% local functions for exact solution
+function y = exactSolution(x)
+ [phi, r] = cart2pol(x(1,:,:), x(2,:,:));
+ phi = phi + 2*pi*(phi < 0);
+ y = r.^(2/3) .* sin(2/3 * phi);
+end
+
+function y = exactSolutionNeumannData(x)
+ x1 = x(1,:,:);
+ x2 = x(2,:,:);
+
+ % determine boundary partsexactSolutionNeumannData
+ right = (x1 > 0) & (abs(x1) > abs(x2));
+ left = (x1 < 0) & (abs(x1) > abs(x2));
+ top = (x2 > 0) & (abs(x1) < abs(x2));
+ bottom = (x2 < 0) & (abs(x1) < abs(x2));
+
+ % compute d/dn uex
+ [phi, r] = cart2pol(x(1,:,:), x(2,:,:));
+ Cr = 2/3 * r.^(-4/3);
+ Cphi = 2/3 * (phi + 2*pi*(phi < 0));
+ dudx = Cr .* (x1.*sin(Cphi) - x2.*cos(Cphi));
+ dudy = Cr .* (x2.*sin(Cphi) + x1.*cos(Cphi));
+
+ y = zeros(size(x1));
+ y(right) = dudx(right);
+ y(left) =-dudx(left);
+ y(top) = dudy(top);
+ y(bottom) =-dudy(bottom);
+end
+
+function indicators = estimate(blf, lf, u)
+p = u.fes.finiteElement.order;
+mesh = u.fes.mesh;
+trafo = getAffineTransformation(mesh);
+
+% compute volume residual element-wise
+% For p=1, the diffusion term vanishes in the residual.
+f = CompositeFunction(@(a, v, f) (a .* (v(1,:,:) + v(4,:,:)) + f).^2, blf.a, Hessian(u), lf.f);
+qr = QuadratureRule.ofOrder(2*p);
+volumeResidual = integrateElement(f, qr);
+
+% compute edge residual edge-wise
+f = CompositeFunction(@(a, Du, fvec) a .* Du - fvec , blf.a, Gradient(u), lf.fvec);
+qr = QuadratureRule.ofOrder(2*max(p-1, 1), '1D');
+edgeResidual = integrateNormalJump(f, qr, ...
+ @(j) zeros(size(j)), {}, mesh.boundaries{1}, ... % no jump on dirichlet edges
+ @(j, phi) j-phi, {lf.neumann}, mesh.boundaries{2},...
+ @(j) j.^2, {}, ':');
+
+% combine the residuals suitably
+hT = sqrt(trafo.area);
+indicators = hT.^2 .* volumeResidual + ...
+ hT .* sum(edgeResidual(mesh.element2edges), Dim.Vector);
+end
+
+function [A, F] = assembleAll(blf, lf, fes)
+freeDofs = getFreeDofs(fes);
+A = assemble(blf, fes);
+A = A(freeDofs, freeDofs);
+
+F = assemble(lf, fes);
+F = F(freeDofs);
+end
+
+function e = energyNorm(A, v)
+e = sqrt(v' * A * v);
+end
\ No newline at end of file
diff --git a/experiments/dataAdaptiveErrorElementwise.aux b/experiments/dataAdaptiveErrorElementwise.aux
new file mode 100644
index 0000000000000000000000000000000000000000..b64012178f9cbc148dca209ceaf227aee4833711
--- /dev/null
+++ b/experiments/dataAdaptiveErrorElementwise.aux
@@ -0,0 +1,2 @@
+\relax
+\gdef \@abspage@last{1}
diff --git a/experiments/dataAdaptiveErrorElementwise.fdb_latexmk b/experiments/dataAdaptiveErrorElementwise.fdb_latexmk
new file mode 100644
index 0000000000000000000000000000000000000000..5ad580273b44cfbd8b2beec2fe7adb3bec5ef230
--- /dev/null
+++ b/experiments/dataAdaptiveErrorElementwise.fdb_latexmk
@@ -0,0 +1,145 @@
+# Fdb version 4
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+\draw[meshStyle, fill=cobalt!18.106212!white] (P24) -- (P44) -- (P48) -- cycle;
+\end{tikzpicture}
+
+ \end{document}
+
+\documentclass{standalone}
+
+\usepackage{tikz}
+
+ \usepackage{pgfplots}
+
+\usepackage{xcolor}
+
+ \definecolor{cobalt}{RGB}{0,102,153}
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+ \definecolor{cobaltred}{RGB}{255, 255,255}
+
+\usepgfplotslibrary{colormaps}
+
+ \begin{document}
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+\end{tikzpicture}
+
+ \end{document}
+
+\documentclass{standalone}
+
+\usepackage{tikz}
+
+ \usepackage{pgfplots}
+
+\usepackage{xcolor}
+
+ \definecolor{cobalt}{RGB}{0,102,153}
+
+ \definecolor{cobaltred}{RGB}{255, 255,255}
+
+\usepgfplotslibrary{colormaps}
+
+ \begin{document}
+
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+\draw[meshStyle, fill=cobalt!17.819764!white] (P18) -- (P41) -- (P53) -- cycle;
+\draw[meshStyle, fill=cobalt!7.148319!white] (P64) -- (P35) -- (P68) -- cycle;
+\draw[meshStyle, fill=cobalt!7.629561!white] (P36) -- (P64) -- (P68) -- cycle;
+\draw[meshStyle, fill=cobalt!2.526222!white] (P64) -- (P18) -- (P52) -- cycle;
+\draw[meshStyle, fill=cobalt!5.214310!white] (P35) -- (P64) -- (P52) -- cycle;
+\draw[meshStyle, fill=cobalt!1.121486!white] (P120) -- (P51) -- (P124) -- cycle;
+\draw[meshStyle, fill=cobalt!1.499946!white] (P54) -- (P120) -- (P124) -- cycle;
+\draw[meshStyle, fill=cobalt!7.941756!white] (P35) -- (P51) -- (P120) -- cycle;
+\draw[meshStyle, fill=cobalt!13.652102!white] (P80) -- (P51) -- (P79) -- cycle;
+\draw[meshStyle, fill=cobalt!75.592392!white] (P5) -- (P80) -- (P79) -- cycle;
+\draw[meshStyle, fill=cobalt!4.789980!white] (P80) -- (P54) -- (P124) -- cycle;
+\draw[meshStyle, fill=cobalt!4.531658!white] (P51) -- (P80) -- (P124) -- cycle;
+\draw[meshStyle, fill=cobalt!7.885778!white] (P54) -- (P36) -- (P68) -- cycle;
+\draw[meshStyle, fill=cobalt!7.395207!white] (P68) -- (P35) -- (P120) -- cycle;
+\draw[meshStyle, fill=cobalt!6.938049!white] (P54) -- (P68) -- (P120) -- cycle;
+\draw[meshStyle, fill=cobalt!24.877416!white] (P36) -- (P19) -- (P45) -- cycle;
+\draw[meshStyle, fill=cobalt!11.331669!white] (P45) -- (P18) -- (P64) -- cycle;
+\draw[meshStyle, fill=cobalt!21.491716!white] (P36) -- (P45) -- (P64) -- cycle;
+\draw[meshStyle, fill=cobalt!2.056299!white] (P81) -- (P17) -- (P114) -- cycle;
+\draw[meshStyle, fill=cobalt!7.447252!white] (P19) -- (P81) -- (P114) -- cycle;
+\draw[meshStyle, fill=cobalt!2.936599!white] (P81) -- (P4) -- (P78) -- cycle;
+\draw[meshStyle, fill=cobalt!2.343593!white] (P17) -- (P81) -- (P78) -- cycle;
+\draw[meshStyle, fill=cobalt!32.115104!white] (P17) -- (P3) -- (P41) -- cycle;
+\draw[meshStyle, fill=cobalt!15.010582!white] (P41) -- (P19) -- (P114) -- cycle;
+\draw[meshStyle, fill=cobalt!10.515097!white] (P17) -- (P41) -- (P114) -- cycle;
+\draw[meshStyle, fill=cobalt!37.766496!white] (P14) -- (P3) -- (P17) -- cycle;
+\draw[meshStyle, fill=cobalt!3.802453!white] (P73) -- (P17) -- (P78) -- cycle;
+\draw[meshStyle, fill=cobalt!0.015332!white] (P4) -- (P73) -- (P78) -- cycle;
+\draw[meshStyle, fill=cobalt!7.729369!white] (P14) -- (P17) -- (P73) -- cycle;
+\draw[meshStyle, fill=cobalt!11.384914!white] (P14) -- (P1) -- (P13) -- cycle;
+\draw[meshStyle, fill=cobalt!30.003981!white] (P3) -- (P14) -- (P13) -- cycle;
+\draw[meshStyle, fill=cobalt!5.470840!white] (P42) -- (P20) -- (P108) -- cycle;
+\draw[meshStyle, fill=cobalt!6.701113!white] (P19) -- (P42) -- (P108) -- cycle;
+\draw[meshStyle, fill=cobalt!8.660664!white] (P42) -- (P7) -- (P82) -- cycle;
+\draw[meshStyle, fill=cobalt!8.521421!white] (P20) -- (P42) -- (P82) -- cycle;
+\draw[meshStyle, fill=cobalt!2.244809!white] (P81) -- (P20) -- (P83) -- cycle;
+\draw[meshStyle, fill=cobalt!3.528680!white] (P4) -- (P81) -- (P83) -- cycle;
+\draw[meshStyle, fill=cobalt!9.755168!white] (P81) -- (P19) -- (P108) -- cycle;
+\draw[meshStyle, fill=cobalt!3.673351!white] (P20) -- (P81) -- (P108) -- cycle;
+\draw[meshStyle, fill=cobalt!16.436585!white] (P47) -- (P36) -- (P65) -- cycle;
+\draw[meshStyle, fill=cobalt!11.901687!white] (P23) -- (P47) -- (P65) -- cycle;
+\draw[meshStyle, fill=cobalt!25.303540!white] (P19) -- (P36) -- (P47) -- cycle;
+\draw[meshStyle, fill=cobalt!6.219960!white] (P70) -- (P54) -- (P121) -- cycle;
+\draw[meshStyle, fill=cobalt!3.446707!white] (P38) -- (P70) -- (P121) -- cycle;
+\draw[meshStyle, fill=cobalt!10.106166!white] (P36) -- (P54) -- (P70) -- cycle;
+\draw[meshStyle, fill=cobalt!3.889423!white] (P80) -- (P56) -- (P126) -- cycle;
+\draw[meshStyle, fill=cobalt!6.808460!white] (P54) -- (P80) -- (P126) -- cycle;
+\draw[meshStyle, fill=cobalt!100.000000!white] (P80) -- (P5) -- (P88) -- cycle;
+\draw[meshStyle, fill=cobalt!35.398996!white] (P56) -- (P80) -- (P88) -- cycle;
+\draw[meshStyle, fill=cobalt!2.888255!white] (P121) -- (P56) -- (P89) -- cycle;
+\draw[meshStyle, fill=cobalt!1.970253!white] (P38) -- (P121) -- (P89) -- cycle;
+\draw[meshStyle, fill=cobalt!4.692596!white] (P121) -- (P54) -- (P126) -- cycle;
+\draw[meshStyle, fill=cobalt!1.851772!white] (P56) -- (P121) -- (P126) -- cycle;
+\draw[meshStyle, fill=cobalt!3.823246!white] (P65) -- (P38) -- (P57) -- cycle;
+\draw[meshStyle, fill=cobalt!3.364392!white] (P23) -- (P65) -- (P57) -- cycle;
+\draw[meshStyle, fill=cobalt!15.219297!white] (P65) -- (P36) -- (P70) -- cycle;
+\draw[meshStyle, fill=cobalt!9.527346!white] (P38) -- (P65) -- (P70) -- cycle;
+\draw[meshStyle, fill=cobalt!38.865709!white] (P23) -- (P7) -- (P42) -- cycle;
+\draw[meshStyle, fill=cobalt!18.847853!white] (P42) -- (P19) -- (P47) -- cycle;
+\draw[meshStyle, fill=cobalt!23.323464!white] (P23) -- (P42) -- (P47) -- cycle;
+\draw[meshStyle, fill=cobalt!23.110146!white] (P43) -- (P23) -- (P46) -- cycle;
+\draw[meshStyle, fill=cobalt!18.580810!white] (P25) -- (P43) -- (P46) -- cycle;
+\draw[meshStyle, fill=cobalt!38.899931!white] (P7) -- (P23) -- (P43) -- cycle;
+\draw[meshStyle, fill=cobalt!9.379806!white] (P66) -- (P38) -- (P69) -- cycle;
+\draw[meshStyle, fill=cobalt!15.009735!white] (P40) -- (P66) -- (P69) -- cycle;
+\draw[meshStyle, fill=cobalt!3.364537!white] (P66) -- (P23) -- (P57) -- cycle;
+\draw[meshStyle, fill=cobalt!3.824091!white] (P38) -- (P66) -- (P57) -- cycle;
+\draw[meshStyle, fill=cobalt!1.879347!white] (P122) -- (P56) -- (P125) -- cycle;
+\draw[meshStyle, fill=cobalt!4.643390!white] (P59) -- (P122) -- (P125) -- cycle;
+\draw[meshStyle, fill=cobalt!1.971055!white] (P122) -- (P38) -- (P89) -- cycle;
+\draw[meshStyle, fill=cobalt!2.923867!white] (P56) -- (P122) -- (P89) -- cycle;
+\draw[meshStyle, fill=cobalt!35.340964!white] (P93) -- (P56) -- (P88) -- cycle;
+\draw[meshStyle, fill=cobalt!99.893894!white] (P5) -- (P93) -- (P88) -- cycle;
+\draw[meshStyle, fill=cobalt!7.009088!white] (P93) -- (P59) -- (P125) -- cycle;
+\draw[meshStyle, fill=cobalt!3.823356!white] (P56) -- (P93) -- (P125) -- cycle;
+\draw[meshStyle, fill=cobalt!9.881019!white] (P59) -- (P40) -- (P69) -- cycle;
+\draw[meshStyle, fill=cobalt!3.401231!white] (P69) -- (P38) -- (P122) -- cycle;
+\draw[meshStyle, fill=cobalt!6.123676!white] (P59) -- (P69) -- (P122) -- cycle;
+\draw[meshStyle, fill=cobalt!24.920458!white] (P40) -- (P25) -- (P46) -- cycle;
+\draw[meshStyle, fill=cobalt!11.740735!white] (P46) -- (P23) -- (P66) -- cycle;
+\draw[meshStyle, fill=cobalt!16.251597!white] (P40) -- (P46) -- (P66) -- cycle;
+\draw[meshStyle, fill=cobalt!3.623420!white] (P94) -- (P29) -- (P115) -- cycle;
+\draw[meshStyle, fill=cobalt!10.340095!white] (P25) -- (P94) -- (P115) -- cycle;
+\draw[meshStyle, fill=cobalt!3.763183!white] (P94) -- (P10) -- (P97) -- cycle;
+\draw[meshStyle, fill=cobalt!2.153612!white] (P29) -- (P94) -- (P97) -- cycle;
+\draw[meshStyle, fill=cobalt!8.490943!white] (P43) -- (P29) -- (P98) -- cycle;
+\draw[meshStyle, fill=cobalt!8.646098!white] (P7) -- (P43) -- (P98) -- cycle;
+\draw[meshStyle, fill=cobalt!6.571413!white] (P43) -- (P25) -- (P115) -- cycle;
+\draw[meshStyle, fill=cobalt!5.517126!white] (P29) -- (P43) -- (P115) -- cycle;
+\draw[meshStyle, fill=cobalt!1.627512!white] (P103) -- (P29) -- (P109) -- cycle;
+\draw[meshStyle, fill=cobalt!2.881933!white] (P32) -- (P103) -- (P109) -- cycle;
+\draw[meshStyle, fill=cobalt!4.904814!white] (P103) -- (P7) -- (P98) -- cycle;
+\draw[meshStyle, fill=cobalt!5.052183!white] (P29) -- (P103) -- (P98) -- cycle;
+\draw[meshStyle, fill=cobalt!1.304336!white] (P100) -- (P29) -- (P97) -- cycle;
+\draw[meshStyle, fill=cobalt!0.314725!white] (P10) -- (P100) -- (P97) -- cycle;
+\draw[meshStyle, fill=cobalt!1.220403!white] (P100) -- (P32) -- (P109) -- cycle;
+\draw[meshStyle, fill=cobalt!2.323291!white] (P29) -- (P100) -- (P109) -- cycle;
+\draw[meshStyle, fill=cobalt!16.244839!white] (P32) -- (P9) -- (P28) -- cycle;
+\draw[meshStyle, fill=cobalt!9.728191!white] (P28) -- (P7) -- (P103) -- cycle;
+\draw[meshStyle, fill=cobalt!6.838257!white] (P32) -- (P28) -- (P103) -- cycle;
+\draw[meshStyle, fill=cobalt!6.904767!white] (P28) -- (P21) -- (P104) -- cycle;
+\draw[meshStyle, fill=cobalt!9.718814!white] (P7) -- (P28) -- (P104) -- cycle;
+\draw[meshStyle, fill=cobalt!16.260376!white] (P9) -- (P21) -- (P28) -- cycle;
+\draw[meshStyle, fill=cobalt!2.354967!white] (P84) -- (P20) -- (P116) -- cycle;
+\draw[meshStyle, fill=cobalt!1.215208!white] (P21) -- (P84) -- (P116) -- cycle;
+\draw[meshStyle, fill=cobalt!0.312062!white] (P84) -- (P4) -- (P83) -- cycle;
+\draw[meshStyle, fill=cobalt!1.321192!white] (P20) -- (P84) -- (P83) -- cycle;
+\draw[meshStyle, fill=cobalt!5.061634!white] (P104) -- (P20) -- (P82) -- cycle;
+\draw[meshStyle, fill=cobalt!4.922766!white] (P7) -- (P104) -- (P82) -- cycle;
+\draw[meshStyle, fill=cobalt!2.922107!white] (P104) -- (P21) -- (P116) -- cycle;
+\draw[meshStyle, fill=cobalt!1.616286!white] (P20) -- (P104) -- (P116) -- cycle;
+\draw[meshStyle, fill=cobalt!15.335353!white] (P105) -- (P24) -- (P110) -- cycle;
+\draw[meshStyle, fill=cobalt!16.636702!white] (P22) -- (P105) -- (P110) -- cycle;
+\draw[meshStyle, fill=cobalt!4.405598!white] (P105) -- (P8) -- (P90) -- cycle;
+\draw[meshStyle, fill=cobalt!7.005709!white] (P24) -- (P105) -- (P90) -- cycle;
+\draw[meshStyle, fill=cobalt!6.835114!white] (P118) -- (P39) -- (P119) -- cycle;
+\draw[meshStyle, fill=cobalt!5.372661!white] (P37) -- (P118) -- (P119) -- cycle;
+\draw[meshStyle, fill=cobalt!6.106250!white] (P118) -- (P24) -- (P91) -- cycle;
+\draw[meshStyle, fill=cobalt!1.696174!white] (P39) -- (P118) -- (P91) -- cycle;
+\draw[meshStyle, fill=cobalt!19.315089!white] (P55) -- (P39) -- (P58) -- cycle;
+\draw[meshStyle, fill=cobalt!10.768562!white] (P85) -- (P58) -- (P92) -- cycle;
+\draw[meshStyle, fill=cobalt!7.910471!white] (P5) -- (P85) -- (P92) -- cycle;
+\draw[meshStyle, fill=cobalt!12.159878!white] (P55) -- (P58) -- (P85) -- cycle;
+\draw[meshStyle, fill=cobalt!5.292809!white] (P55) -- (P37) -- (P119) -- cycle;
+\draw[meshStyle, fill=cobalt!8.459901!white] (P39) -- (P55) -- (P119) -- cycle;
+\draw[meshStyle, fill=cobalt!7.108371!white] (P110) -- (P37) -- (P86) -- cycle;
+\draw[meshStyle, fill=cobalt!6.261557!white] (P22) -- (P110) -- (P86) -- cycle;
+\draw[meshStyle, fill=cobalt!11.767949!white] (P110) -- (P24) -- (P118) -- cycle;
+\draw[meshStyle, fill=cobalt!8.314243!white] (P37) -- (P110) -- (P118) -- cycle;
+\draw[meshStyle, fill=cobalt!6.138898!white] (P87) -- (P26) -- (P117) -- cycle;
+\draw[meshStyle, fill=cobalt!4.289883!white] (P22) -- (P87) -- (P117) -- cycle;
+\draw[meshStyle, fill=cobalt!10.012450!white] (P6) -- (P26) -- (P87) -- cycle;
+\draw[meshStyle, fill=cobalt!2.383681!white] (P105) -- (P26) -- (P95) -- cycle;
+\draw[meshStyle, fill=cobalt!4.919243!white] (P8) -- (P105) -- (P95) -- cycle;
+\draw[meshStyle, fill=cobalt!6.008568!white] (P105) -- (P22) -- (P117) -- cycle;
+\draw[meshStyle, fill=cobalt!5.234754!white] (P26) -- (P105) -- (P117) -- cycle;
+\draw[meshStyle, fill=cobalt!2.676673!white] (P106) -- (P26) -- (P111) -- cycle;
+\draw[meshStyle, fill=cobalt!1.766352!white] (P27) -- (P106) -- (P111) -- cycle;
+\draw[meshStyle, fill=cobalt!7.382722!white] (P106) -- (P8) -- (P95) -- cycle;
+\draw[meshStyle, fill=cobalt!2.859634!white] (P26) -- (P106) -- (P95) -- cycle;
+\draw[meshStyle, fill=cobalt!8.334976!white] (P26) -- (P6) -- (P96) -- cycle;
+\draw[meshStyle, fill=cobalt!1.396771!white] (P96) -- (P27) -- (P111) -- cycle;
+\draw[meshStyle, fill=cobalt!1.264958!white] (P26) -- (P96) -- (P111) -- cycle;
+\draw[meshStyle, fill=cobalt!15.410698!white] (P27) -- (P11) -- (P31) -- cycle;
+\draw[meshStyle, fill=cobalt!10.161469!white] (P31) -- (P8) -- (P106) -- cycle;
+\draw[meshStyle, fill=cobalt!8.737881!white] (P27) -- (P31) -- (P106) -- cycle;
+\draw[meshStyle, fill=cobalt!30.783399!white] (P33) -- (P8) -- (P31) -- cycle;
+\draw[meshStyle, fill=cobalt!11.483459!white] (P11) -- (P33) -- (P31) -- cycle;
+\draw[meshStyle, fill=cobalt!8.056717!white] (P30) -- (P33) -- (P101) -- cycle;
+\draw[meshStyle, fill=cobalt!0.000000!white] (P101) -- (P10) -- (P99) -- cycle;
+\draw[meshStyle, fill=cobalt!4.000255!white] (P30) -- (P101) -- (P99) -- cycle;
+\draw[meshStyle, fill=cobalt!38.269279!white] (P8) -- (P33) -- (P30) -- cycle;
+\draw[meshStyle, fill=cobalt!10.756670!white] (P44) -- (P30) -- (P112) -- cycle;
+\draw[meshStyle, fill=cobalt!15.403740!white] (P25) -- (P44) -- (P112) -- cycle;
+\draw[meshStyle, fill=cobalt!32.395533!white] (P8) -- (P30) -- (P44) -- cycle;
+\draw[meshStyle, fill=cobalt!2.200289!white] (P94) -- (P30) -- (P99) -- cycle;
+\draw[meshStyle, fill=cobalt!3.167476!white] (P10) -- (P94) -- (P99) -- cycle;
+\draw[meshStyle, fill=cobalt!7.996605!white] (P94) -- (P25) -- (P112) -- cycle;
+\draw[meshStyle, fill=cobalt!1.922313!white] (P30) -- (P94) -- (P112) -- cycle;
+\draw[meshStyle, fill=cobalt!21.502835!white] (P48) -- (P40) -- (P67) -- cycle;
+\draw[meshStyle, fill=cobalt!10.518957!white] (P24) -- (P48) -- (P67) -- cycle;
+\draw[meshStyle, fill=cobalt!24.681125!white] (P25) -- (P40) -- (P48) -- cycle;
+\draw[meshStyle, fill=cobalt!6.397044!white] (P71) -- (P59) -- (P123) -- cycle;
+\draw[meshStyle, fill=cobalt!6.621833!white] (P39) -- (P71) -- (P123) -- cycle;
+\draw[meshStyle, fill=cobalt!7.453914!white] (P40) -- (P59) -- (P71) -- cycle;
+\draw[meshStyle, fill=cobalt!4.681438!white] (P93) -- (P58) -- (P127) -- cycle;
+\draw[meshStyle, fill=cobalt!4.996123!white] (P59) -- (P93) -- (P127) -- cycle;
+\draw[meshStyle, fill=cobalt!75.362049!white] (P93) -- (P5) -- (P92) -- cycle;
+\draw[meshStyle, fill=cobalt!13.680165!white] (P58) -- (P93) -- (P92) -- cycle;
+\draw[meshStyle, fill=cobalt!7.978324!white] (P58) -- (P39) -- (P123) -- cycle;
+\draw[meshStyle, fill=cobalt!1.739519!white] (P123) -- (P59) -- (P127) -- cycle;
+\draw[meshStyle, fill=cobalt!0.657834!white] (P58) -- (P123) -- (P127) -- cycle;
+\draw[meshStyle, fill=cobalt!7.074284!white] (P67) -- (P39) -- (P91) -- cycle;
+\draw[meshStyle, fill=cobalt!2.198364!white] (P24) -- (P67) -- (P91) -- cycle;
+\draw[meshStyle, fill=cobalt!7.433268!white] (P67) -- (P40) -- (P71) -- cycle;
+\draw[meshStyle, fill=cobalt!8.065299!white] (P39) -- (P67) -- (P71) -- cycle;
+\draw[meshStyle, fill=cobalt!17.829876!white] (P44) -- (P24) -- (P90) -- cycle;
+\draw[meshStyle, fill=cobalt!9.085265!white] (P8) -- (P44) -- (P90) -- cycle;
+\draw[meshStyle, fill=cobalt!16.722169!white] (P44) -- (P25) -- (P48) -- cycle;
+\draw[meshStyle, fill=cobalt!18.106212!white] (P24) -- (P44) -- (P48) -- cycle;
+\end{tikzpicture}
+
+ \end{document}
+
diff --git a/experiments/saveTikzConformingColor.m b/experiments/saveTikzConformingColor.m
new file mode 100644
index 0000000000000000000000000000000000000000..c78d41db7b8b6b090f8c971d7fce87fd082bf19c
--- /dev/null
+++ b/experiments/saveTikzConformingColor.m
@@ -0,0 +1,53 @@
+function saveTikzConforming(coordinates, elements, additionalData, fileName)
+% saveTikzConforming Save mesh data for later use in TikZ (with LaTeX)
+%
+% Save mesh data in a file suitable for \input{} within a tikzpicture
+% environment in LaTeX.
+% The drawing style is defined in the first line of the output file for
+% convenient manual editing.
+%
+% Usage:
+% saveTikzConforming(coordinates, elements) Save meshdata in file 'mesh.tex'
+%
+% saveTikzConforming(coordinates, elements, fileName) Save meshdata in file with custom name
+
+arguments
+ coordinates (:,2) double
+ elements (:,3) double
+ additionalData (:,1) double
+ fileName (1,1) string = 'meshWithData.tex'
+end
+
+minData = min(additionalData);
+maxUpdatedData = max(additionalData - minData);
+additionalDataUpdate = abs((additionalData - minData)/maxUpdatedData)*100;
+
+%% open file
+fileID = fopen(fileName, 'a');
+assert(fileID ~= -1, 'Cannot open file %s.', fileName)
+
+fprintf(fileID, '\\documentclass{standalone}\n\n');
+
+
+fprintf(fileID, '\\usepackage{tikz} \n \n \\usepackage{pgfplots}\n\n');
+
+fprintf(fileID, '\\usepackage{xcolor} \n \n \\definecolor{cobalt}{RGB}{0,102,153} \n\n \\definecolor{cobaltred}{RGB}{255, 255,255} \n \n');
+
+fprintf(fileID, '\\usepgfplotslibrary{colormaps} \n \n \\begin{document} \n\n \\begin{tikzpicture} \n \n');
+
+
+fprintf(fileID, '\\tikzset{meshStyle/.style={very thin, lightgray}}\n\n');
+
+%% define coordinates in tikz
+nCoordinates = size(coordinates, 1);
+fprintf(fileID, '\\coordinate (P%d) at (%.4g,%.4g);\n', [(1:nCoordinates)', coordinates]');
+fprintf(fileID, '\n');
+
+%% draw mesh lines
+fprintf(fileID, '\\draw[meshStyle, fill=cobalt!%f!white] (P%d) -- (P%d) -- (P%d) -- cycle;\n',[additionalDataUpdate, elements]');
+
+fprintf(fileID, '\\end{tikzpicture} \n\n \\end{document} \n \n');
+
+%% close file
+fclose(fileID);
+end