An a posteriori residual error estimator for the finite element method on anisotropic tetrahedral meshes
A new a posteriori residual error estimator is defined and analyzed for anisotropic tetrahedral finite element meshes. All considerations carry over to anisotropic triangular meshes with minor changes only. The lower error bound is obtained by means of bubble functions and the corresponding anisotropic inverse inequalities. To prove the upper error bound, it is vital that an anisotropic mesh corresponds to the anisotropic function under consideration. Making use of this correspondence anisotropic interpolation estimates and subsequently the upper error bound are proved. A numerical example confirms the theoretical analysis.
scientific article; zbMATH DE number 1538608