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Discrete Conservation Of Nonnegativity For Elliptic Problems Solved By The Hp-Fem, Pavel Solin, Thomas Vejchodsky, Roberto Araiza
Discrete Conservation Of Nonnegativity For Elliptic Problems Solved By The Hp-Fem, Pavel Solin, Thomas Vejchodsky, Roberto Araiza
Departmental Technical Reports (CS)
Most results related to discrete nonnegativity conservation principles (DNCP) for elliptic problems are limited to finite differences (FDM) and lowest-order finite element methods (FEM). In this paper we confirm that a straightforward extension to higher-order finite element methods (hp-FEM) in the classical sense is not possible. We formulate a weaker DNCP for the Poisson equation in one spatial dimension and prove it using an interval computing technique. Numerical experiments related to the extension of this result to 2D are presented.