Approximation of diffusion operators with discontinuous tensor coefficients on distorted meshes. (English) Zbl 1037.65118
From the author’s abstract: A new finite volume method is presented for discretizing diffusion operators with discontinuous tensor coefficients. The main advantages of this method is that arbitrary distorted meshes can be used without the numerical results being altered. The matrices that need to be inverted are positive definite, so the most powerful linear solvers can be applied. Moreover, the numerical experiments show that the method is second-order accurate. The method has been tested on a few elliptic and parabolic equations.
Reviewer: Xavier Antoine (Toulouse)
MSC:
| 65N30 | Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs |
| 35K15 | Initial value problems for second-order parabolic equations |
| 65M06 | Finite difference methods for initial value and initial-boundary value problems involving PDEs |
| 65M50 | Mesh generation, refinement, and adaptive methods for the numerical solution of initial value and initial-boundary value problems involving PDEs |
| 65N50 | Mesh generation, refinement, and adaptive methods for boundary value problems involving PDEs |
| 35J25 | Boundary value problems for second-order elliptic equations |
| 35R05 | PDEs with low regular coefficients and/or low regular data |
Keywords:
elliptic equation; parabolic equation; finite volume method; Lagrangian mesh; diffusion operators; discontinuous tensor coefficients; numerical resultsReferences:
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