Academic problems

An original adaptive algorithm has been proposed, based on an anisotropic error estimator valid for highly stretched meshes. It has been proved and checked numerically that the effectivity index (the ratio between the estimated and true errors) is aspect ratio independent on adapted, highly stretched meshes (aspect ratio up to 100 000). The method has been applied to elliptic problems but also to convection-dominated problems and to nonlinear parabolic problems arising from solidification.

Below is an example of mesh adaptation in an academic stretching problem.