Discretization of coupled heat and electrical diffusion problems by finite-element and finite-volume methods. (English) Zbl 1144.78024

Bradji, Abdallah; Herbin, Raphaèle

IMA J. Numer. Anal. 28, No. 3, 469-495 (2008).

This paper deals with the coupled heat and potential equation and the authors are concerned with the convergence of a cell-centered finite-volume method and linear finite-element method for this class of nonlinear problems. In the case of the cell-centered finite volume, the scheme satisfies the maximum principle for any admissible mesh. The techniques of proofs are very related to the tools used for the proof of existence in the continuous case, which requires the monotonicity of the operator.

Reviewer: Teodora-Liliana Rădulescu (Craiova)

MSC:

78M10	Finite element, Galerkin and related methods applied to problems in optics and electromagnetic theory
78A30	Electro- and magnetostatics
35J45	Systems of elliptic equations, general (MSC2000)
78M25	Numerical methods in optics (MSC2010)

Keywords:

nonlinear elliptic system; diffusion equation; finite-element scheme; finite-volume scheme; \(L^1\)-data; Ohmic losses