Some abstract error estimates of a finite volume scheme for a nonstationary heat equation on general nonconforming multidimensional spatial meshes.

DOI10.1007/s10492-013-0001-yzbMath1274.65251OpenAlexW2039783631MaRDI QIDQ1950791

Abdallah Bradji, Jürgen Fuhrmann

Publication date: 13 May 2013

Published in: Applications of Mathematics (Search for Journal in Brave)

Full work available at URL: http://hdl.handle.net/10338.dmlcz/143131

zbMATH Keywords

heat equationfinite volume methoderror estimateSUSHI schemediscrete gradientnonconforming gridsstar-shaped elements

Mathematics Subject Classification ID

Heat equation (35K05) Error bounds for initial value and initial-boundary value problems involving PDEs (65M15) Mesh generation, refinement, and adaptive methods for the numerical solution of initial value and initial-boundary value problems involving PDEs (65M50) Finite volume methods for initial value and initial-boundary value problems involving PDEs (65M08)

Related Items (16)

An analysis of a second-order time accurate scheme for a finite volume method for parabolic equations on general nonconforming multidimensional spatial meshes ⋮ The generalized finite volume SUSHI scheme for the discretization of the Peaceman model. ⋮ A full analysis of a new second order finite volume approximation based on a low-order scheme using general admissible spatial meshes for the unsteady one dimensional heat equation ⋮ Steady-state inhomogeneous diffusion with generalized oblique boundary conditions ⋮ A New Optimal $$L^{\infty }(H^1)$$–Error Estimate of a SUSHI Scheme for the Time Fractional Diffusion Equation ⋮ Unnamed Item ⋮ A Convergence Result of a Linear SUSHI Scheme Using Characteristics Method for a Semi-linear Parabolic Equation ⋮ Convergence Analysis of a Finite Volume Gradient Scheme for a Linear Parabolic Equation Using Characteristic Methods ⋮ A priori error estimates for upwind finite volume schemes for two-dimensional linear convection diffusion problems ⋮ Error estimates for higher-order finite volume schemes for convection-diffusion problems ⋮ An analysis for the convergence order of gradient schemes for semilinear parabolic equations ⋮ On the convergence and convergence order of finite volume gradient schemes for oblique derivative boundary value problems ⋮ Two new error estimates of a fully discrete primal-dual mixed finite element scheme for parabolic equations in any space dimension ⋮ A Theoretical Analysis for a New Finite Volume Scheme for a Linear Schrödinger Evolution Equation on General Nonconforming Spatial Meshes ⋮ On gradient structures for Markov chains and the passage to Wasserstein gradient flows ⋮ Convergence Order of a Finite Volume Scheme for the Time-Fractional Diffusion Equation

Cites Work

• Unnamed Item
• Error estimates of the discretization of linear parabolic equations on general nonconforming spatial grids
• A new finite volume scheme for anisotropic diffusion problems on general grids: convergence analysis
• Some simple error estimates of finite volume approximate solution for parabolic equations
• Discretization of heterogeneous and anisotropic diffusion problems on general nonconforming meshes SUSHI: a scheme using stabilization and hybrid interfaces
• Discretization of coupled heat and electrical diffusion problems by finite-element and finite-volume methods
• An optimal L (L2)-error estimate for the discontinuous Galerkin approximation of a nonlinear non-stationary convection-diffusion problem
• Parabolic finite volume element equations in nonconvex polygonal domains
• Cell centred discretisation of non linear elliptic problems on general multidimensional polyhedral grids
• Error Estimates on the Approximate Finite Volume Solution of Convection Diffusion Equations with General Boundary Conditions
• Error estimates for a finite volume element method for parabolic equations in convex polygonal domains
• A cell-centred finite-volume approximation for anisotropic diffusion operators on unstructured meshes in any space dimension
• Galerkin Finite Element Methods for Parabolic Problems

This page was built for publication: Some abstract error estimates of a finite volume scheme for a nonstationary heat equation on general nonconforming multidimensional spatial meshes.