Numerical conservation and discrete maximum principle for Elliptic PDEs

Enrico Bertolazzi

Abstract

A class of finite volume numerical schemes for the solution of selfadjoint elliptic equations is described. The main feature of the schemes is that numerical solutions share both discrete conservation and discrete strong maximum principle without restriction on the differential operator or on the volume elements.

keywords

Discrete maximum principle, discrete conservation, M-matrix, Brouwer fixed point.

DOI: https://www.doi.org/10.1142/S0218202598000317

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