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Unified analysis of higher-order finite volume methods for parabolic problems on quadrilateral meshes. (English) Zbl 1433.65179

Summary: In this paper, a unified analysis for higher-order finite volume methods for parabolic problems on quadrilateral meshes is presented. By studying the quasi-symmetry of the finite volume bilinear form, optimal-order error estimates in the \( L^\infty (H^1)\)- and \(L^\infty (L^2)\)-norms are derived. The theoretical estimates are validated by numerical experiments.

MSC:

65M08 Finite volume methods for initial value and initial-boundary value problems involving PDEs
65M15 Error bounds for initial value and initial-boundary value problems involving PDEs
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