Discrete conservation of nonnegativity for elliptic problems solved by the hp-FEM

0335936 - MÚ 2010 RIV NL eng J - Journal Article
Šolín, P. - Vejchodský, Tomáš - Araiza, R.
Discrete conservation of nonnegativity for elliptic problems solved by the hp-FEM.
Mathematics and Computers in Simulation. Roč. 76, 1-3 (2007), s. 205-210. ISSN 0378-4754. E-ISSN 1872-7166
R&D Projects: GA ČR GP201/04/P021
Institutional research plan: CEZ:AV0Z10190503
Keywords : discrete nonnegativity conservation * discrete Green's function * elliptic problems * hp-FEM * higher-order finite element methods * Poisson equation * numerical experimetns
Subject RIV: BA - General Mathematics
Impact factor: 0.738, year: 2007

Most results related to discrete nonnegativity conservation principles (DNCP) for elliptic problems are limited to finite differences and lowest-order finite element methods (FEM). In this paper we show that a straightforward extension of this principle 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.
Permanent Link: http://hdl.handle.net/11104/0180279