Displaying similar documents to “ L 2 -stability of the upwind first order finite volume scheme for the Maxwell equations in two and three dimensions on arbitrary unstructured meshes”

-stability of the upwind first order finite volume scheme for the Maxwell equations in two and three dimensions on arbitrary unstructured meshes

Serge Piperno (2010)

ESAIM: Mathematical Modelling and Numerical Analysis

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We investigate sufficient and possibly necessary conditions for the stability of the upwind first order finite volume scheme for Maxwell equations, with metallic and absorbing boundary conditions. We yield a very general sufficient condition, valid for any finite volume partition in two and three space dimensions. We show this condition is necessary for a class of regular meshes in two space dimensions. However, numerical tests show it is not necessary in three space...

A stability analysis for finite volume schemes applied to the Maxwell system

Sophie Depeyre (2010)

ESAIM: Mathematical Modelling and Numerical Analysis

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We present in this paper a stability study concerning finite volume schemes applied to the two-dimensional Maxwell system, using rectangular or triangular meshes. A stability condition is proved for the first-order upwind scheme on a rectangular mesh. Stability comparisons between the Yee scheme and the finite volume formulation are proposed. We also compare the stability domains obtained when considering the Maxwell system and the convection equation.

Convergence and stability of a discontinuous Galerkin time-domain method for the 3D heterogeneous Maxwell equations on unstructured meshes

Loula Fezoui, Stéphane Lanteri, Stéphanie Lohrengel, Serge Piperno (2005)

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique

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A Discontinuous Galerkin method is used for to the numerical solution of the time-domain Maxwell equations on unstructured meshes. The method relies on the choice of local basis functions, a centered mean approximation for the surface integrals and a second-order leap-frog scheme for advancing in time. The method is proved to be stable for cases with either metallic or absorbing boundary conditions, for a large class of basis functions. A discrete analog of the electromagnetic energy...