论文信息 - Analysis of the Cell-Vertex Finite Volume Method for Hyperbolic Problems with Variable Coefficients

Analysis of the Cell-Vertex Finite Volume Method for Hyperbolic Problems with Variable Coefficients

An analysis of the cell-vertex finite volume method is presented for a scalar linear hyperbolic equation with variable coefficients. The cell-vertex approximation is shown to be second-order convergent in the L2-norm and first-order convergent in the H1-norm, provided the exact solution belongs to H3 and the characteristic curves of the differential equation are transversal to mesh lines on the closure of the domain of integration. When characteristics are parallel to mesh lines on a subset of positive measure the scheme is only first-order convergent in the L2-norm. However, if transversality fails on part of the outflow boundary only, then the cell-vertex scheme is second-order convergent in a weighted L2-norm.

Endre Süli | Philippe Balland

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