Error estimation of a quadratic finite volume method on right quadrangular prism grids

DOI10.1016/j.cam.2008.10.036zbMath1167.65062OpenAlexW1986193655MaRDI QIDQ1023332

Jiangguo Liu, Min Yang, Chuanjun Chen

Publication date: 11 June 2009

Published in: Journal of Computational and Applied Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.cam.2008.10.036

zbMATH Keywords

Dirichlet problemerror estimatesnumerical exampleslinear elliptic equationssecond order accuracyfinite volume element methodsquadratic basesright quadrangular prism meshes

Mathematics Subject Classification ID

Boundary value problems for second-order elliptic equations (35J25) Error bounds for boundary value problems involving PDEs (65N15) Stability and convergence of numerical methods for boundary value problems involving PDEs (65N12) Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs (65N30) Mesh generation, refinement, and adaptive methods for boundary value problems involving PDEs (65N50)

Related Items (7)

Cubic superconvergent finite volume element method for one-dimensional elliptic and parabolic equations ⋮ Three dimensional high order finite volume element schemes for elliptic equations ⋮ Augmented high order finite volume element method for elliptic PDEs in non-smooth domains: Convergence study ⋮ Some recent advances on vertex centered finite volume element methods for elliptic equations ⋮ Optimal Bicubic Finite Volume Methods on Quadrilateral Meshes ⋮ A spectral method for triangular prism ⋮ Superconvergent biquadratic finite volume element method for two-dimensional Poisson's equations

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• The upwind finite volume element method based on straight triangular prism partition for nonlinear convection-diffusion problem
• Spectral (finite) volume method for conservation laws on unstructured grids. Basic formulation
• Finite volume element methods for non-definite problems
• Development and analysis of higher order finite volume methods over rectangles for elliptic equations
• The finite volume element method with quadratic basis functions
• A second-order finite volume element method on quadrilateral meshes for elliptic equations
• Unified Analysis of Finite Volume Methods for Second Order Elliptic Problems
• The Accuracy of Cell Vertex Finite Volume Methods on Quadrilateral Meshes
• On the Finite Volume Element Method for General Self-Adjoint Elliptic Problems
• Finite Volume Methods for Elliptic PDE's: A New Approach
• High-order Finite Difference and Finite Volume WENO Schemes and Discontinuous Galerkin Methods for CFD
• On the Accuracy of the Finite Volume Element Method Based on Piecewise Linear Polynomials
• On the Construction and Analysis of High Order Locally Conservative Finite Volume-Type Methods for One-Dimensional Elliptic Problems
• Error estimates in $L^2$, $H^1$ and $L^\infty$ in covolume methods for elliptic and parabolic problems: A unified approach

This page was built for publication: Error estimation of a quadratic finite volume method on right quadrangular prism grids