Discrete maximum principle for a 1D problem with piecewise-constant coefficients solved by hp-FEM

Journal article

In this paper we prove the discrete maximum principle for a one-dimensional equation of the form (au) = f with piecewise-constant coefficient a(x), discretized by the hp-FEM. The discrete problem is transformed in such a way that the discontinuity of the coefficient a(x) disappears. Existing results are then applied to obtain a condition on the mesh which guarantees the satisfaction of the discrete maximum principle. Both Dirichlet and mixed DirichletNeumann boundary conditions are discussed. © de Gruyter 2007.

Authors: Vejchodský, T; ŠOlín, P

• Journal: Journal of Numerical Mathematics
• Volume: 15
• Issue: 3
• Pages: 233-243
• Publication date: 2007-10-10
• DOI: 10.1515/jnma.2007.011
• EISSN: 1569-3953
• ISSN: 1570-2820