Abstract
A nonlinear correction technique for finite element methods to anisotropic diffusion problems on general triangular and quadrilateral meshes are introduced. The classic linear or bi-linear finite element methods are modified, and then the resulting schemes satisfy the discrete strong extremum principle unconditionally, which means that it is unnecessary to impose the well-known restrictions on diffusion coefficients and geometry of mesh-cell (e.g. “acute angle” condition). Convergence rate for smooth and piecewise smooth solutions and the discrete extremum principle property are verified by numerical examples.
Published Version
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