A posteriori L-2 error estimation on anisotropic tetrahedral finite element meshes

A new a posteriori L-2 norm error estimator is proposed for the Poisson equ ation. The error estimator can be applied to anisotropic tetrahedral or tri angular finite element meshes. The estimator is rigorously analysed for Dir ichlet and Neumann boundary conditions. The lower error bound relies on specifically designed anisotropic bubble fu nctions and the corresponding inverse inequalities. The upper error bound u tilizes non-standard anisotropic interpolation estimates. Its proof require s H-2 regularity of the Poisson problem, and its quality depends on how goo d the anisotropic mesh resolves the anisotropy of the problem. This is meas ured by a so-called 'matching function'. A numerical example supports the anisotropic error analysis.