Discontinuous finite volume element method for parabolic problems

DOI10.1002/num.20437zbMath1189.65203OpenAlexW2171244464MaRDI QIDQ5187888

Jiaqiang Geng, Chunjia Bi

Publication date: 9 March 2010

Published in: Numerical Methods for Partial Differential Equations (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1002/num.20437

zbMATH Keywords

convergencediscontinuous Galerkin methodssemidiscrete schemebackward Euler methodparabolic problemsfully discrete schemefinite volume element methods\(L^{2}\)-error estimate\(H^{1}\)-error estimate

Mathematics Subject Classification ID

Initial-boundary value problems for second-order parabolic equations (35K20) Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs (65M12) Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs (65M60) Error bounds for initial value and initial-boundary value problems involving PDEs (65M15) Method of lines for initial value and initial-boundary value problems involving PDEs (65M20) Finite volume methods for initial value and initial-boundary value problems involving PDEs (65M08)

Related Items (11)

Discontinuous finite volume element method of two-dimensional unsaturated soil water movement problem ⋮ A Crank-Nicolson discontinuous finite volume element method for a coupled non-stationary Stokes-Darcy problem ⋮ Discontinuous finite volume element method for Darcy flows in fractured porous media ⋮ An adaptive discontinuous finite volume element method for the Allen-Cahn equation ⋮ A discontinuous finite volume method for the Darcy-Stokes equations ⋮ Error bounds for discontinuous finite volume discretisations of Brinkman optimal control problems ⋮ Discontinuous finite volume element method for a coupled non-stationary Stokes-Darcy problem ⋮ Discontinuous finite volume element method for a coupled Navier-Stokes-Cahn-Hilliard phase field model ⋮ Discontinuous approximation of viscous two-phase flow in heterogeneous porous media ⋮ Mixed and discontinuous finite volume element schemes for the optimal control of immiscible flow in porous media ⋮ Discontinuous mixed covolume methods for linear parabolic integrodifferential problems

Cites Work

• Unnamed Item
• On the finite volume element method
• Multigrid algorithms for a vertex-centered covolume method for elliptic problems
• Finite volume element methods for non-definite problems
• Two-grid finite volume element method for linear and nonlinear elliptic problems
• Superconvergence of finite volume element method for a nonlinear elliptic problem
• Unified Analysis of Finite Volume Methods for Second Order Elliptic Problems
• Some Error Estimates for the Box Method
• A Two-Grid Finite Difference Scheme for Nonlinear Parabolic Equations
• Finite Volume Methods for Elliptic PDE's: A New Approach
• Unified Analysis of Discontinuous Galerkin Methods for Elliptic Problems
• On the Accuracy of the Finite Volume Element Method Based on Piecewise Linear Polynomials
• Error estimates for a finite volume element method for parabolic equations in convex polygonal domains
• A New Discontinuous Finite Volume Method for Elliptic Problems
• Pointwise Error Estimates of Discontinuous Galerkin Methods with Penalty for Second-Order Elliptic Problems
• Error estimates in $L^2$, $H^1$ and $L^\infty$ in covolume methods for elliptic and parabolic problems: A unified approach
• Discontinuous Galerkin Methods for Quasi‐Linear Elliptic Problems of Nonmonotone Type
• A Discontinuous Finite Volume Method for the Stokes Problems
• Discontinuous Galerkin finite element approximation of quasilinear elliptic boundary value problems I: the scalar case

This page was built for publication: Discontinuous finite volume element method for parabolic problems