Failure of the discrete maximum principle for an elliptic finite element problem

Abstract

There has been a long-standing question of whether certain mesh restrictions are required for a maximum condition to hold for the discrete equations arising from a finite element approximation of an elliptic problem. This is related to knowing whether the discrete Green’s function is positive for triangular meshes allowing sufficiently good approximation of… (More)
DOI: 10.1090/S0025-5718-04-01651-5

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