Yang, Min; Liu, Jiangguo; Zou, Qingsong Unified analysis of higher-order finite volume methods for parabolic problems on quadrilateral meshes. (English) Zbl 1433.65179 IMA J. Numer. Anal. 36, No. 2, 872-896 (2016). 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. Cited in 7 Documents 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 Keywords:error estimates; finite volume methods; Gaussian points; higher order; parabolic problems; quadrilateral meshes PDFBibTeX XMLCite \textit{M. Yang} et al., IMA J. Numer. Anal. 36, No. 2, 872--896 (2016; Zbl 1433.65179) Full Text: DOI Link