Discrete maximum principle for Galerkin approximations of the Laplace operator on arbitrary meshes

We derive a nonlinear stabilized Galerkin approximation of the Laplace operator for which we prove a discrete maximum principle on arbitrary meshes and for arbitrary space dimension without resorting to the well-known acute condition or generalizations thereof. We also prove the existence of a discrete solution and discuss the extension of the scheme to convection–diffusion–reaction equations. Finally, we present examples showing that the new scheme cures local minima produced by the standard Galerkin approach while maintaining first-order accuracy in the H1-norm.

Published in:
comptes rendus de l'académie des sciences série i: mathématique, 338, 8, 641-646

 Record created 2007-04-24, last modified 2018-03-17

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