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\(L^2\)-stability of the upwind first order finite volume scheme for the Maxwell equations in two and three dimensions on arbitrary unstructured meshes. (English) Zbl 0949.65104

The authors obtain sufficient and possibly necessary conditions for \(L^2\)-stability of the upwind first-order finite volume scheme for Maxwell’s equations, with metallic and absorbing boundary conditions. They obtain a very general sufficient condition, valid for any finite volume partition in two or three space dimensions. They show that this condition is necessary for a class of regular meshes in two space dimensions.

MSC:

65M60 Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs
35Q60 PDEs in connection with optics and electromagnetic theory
78M25 Numerical methods in optics (MSC2010)
78A25 Electromagnetic theory (general)
65M15 Error bounds for initial value and initial-boundary value problems involving PDEs
65M12 Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs

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