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The finite element solution of two-dimensional anisotropic diffusion problemsis considered. A Delaunay-type mesh condition is developed for linear finiteelement approximations to satisfy a discrete maximum principle. The conditionis shown to be weaker than the existing anisotropic non-obtuse angle condition.It reduces to the well known Delaunay condition for the special case with theidentity diffusion matrix. Numerical results are presented to verify thetheoretical findings.

Discrete maximum principle and a Delaunay-type mesh condition for linear  finite element approximations of two-dimensional anisotropic diffusion  problems