Accuracy Tests for COMSOL - and Delaunay Meshes

E. Holzbecher, and Hang Si
Weierstrass Institute for Applied Analysis and Stochastics (WIAS), Berlin, Germany

In the paper we examine the accuracy of various meshes for different model regions and simple differential equations in 2D and in 3D. We study the potential equation for a single irregular domain (2D testcase 1), for a simple domain with irregular sub-domains (2D testcase 2) and a 3D testcase. For testcase 1 we compare with the analytical solution, for testcases 2 with the best solution, obtained by several adaptive grid refinements on a fine mesh. We study meshes obtained by global refinements and by adaptive grid refinement, using various options available in COMSOL Multiphysics. For quadratic elements we find convergence rates between 1 and 1.5, i.e. significantly reduced in comparison to the theoretical rate. Moreover, for testcase 1 we examine imported meshes with Delaunay property and find no advantages in comparison to non-Delaunay meshes for the chosen set-up.