A FV scheme for Maxwell’s equations. Convergence analysis on unstructured meshes. (English) Zbl 1062.78017

Lohrengel, Stephanie; Remaki, Malika

Herbin, Raphaéle (ed.) et al., Finite volumes for complex applications III. Problems and perspectives. Papers from the 3rd symposium of finite volumes for complex applications, Porquerolles, France, June 24–28, 2002. London: Hermes Penton Science (ISBN 1-9039-9634-1/pbk). 219-226 (2002).

Summary: In [COMPEL 19, No. 3, 913–931 (2000; Zbl 0994.78021)] the article the second author developed a new finite volume scheme for the resolution of the heterogeneous Maxwell equations in three dimensions. The scheme is based on a leapfrog time discretization and involves a centered flux formula for discretization in space. Numerical tests have shown the performance of the method, namely on unstructured grids. In this paper, we will present some recent convergence results in \(L^2\) in the case of unstructured grids which satisfy an appropriate “aspect condition”. This condition will be dicussed and illustrated by some numerical results.
For the entire collection see [Zbl 1049.65002].

MSC:

78M25

Numerical methods in optics (MSC2010)

Keywords:

finite volume scheme; centered flux; stability; convergence

Citations:

Zbl 0994.78021