6533b82efe1ef96bd129267b

RESEARCH PRODUCT

Discrete Maximum Principle for Galerkin Finite Element Solutions to Parabolic Problems on Rectangular Meshes

Sergey KorotovRóbert HorváthIstván Faragó

subject

Maximum principleComputer simulationMathematical modelDiscontinuous Galerkin methodBilinear interpolationApplied mathematicsPolygon meshGalerkin methodFinite element methodMathematics

description

One of the most important problems in numerical simulation is the preservation of qualitative properties of solutions of mathematical models. For problems of parabolic type, one of such properties is the maximum principle. In [5], Fujii analyzed the discrete analogue of the (continuous) maximum principle for the linear parabolic problems, and derived sufficient conditions guaranteeing its validity for the Galerkin finite element approximations built on simplicial meshes. In our paper, we present the sufficient conditions for the validity of the discrete maximum principle for the case of bilinear finite element space approximations on rectangular meshes.

yearjournalcountryeditionlanguage
2004-01-01
https://doi.org/10.1007/978-3-642-18775-9_27