Error estimates for a finite volume element method for parabolic equations in convex polygonal domains
From MaRDI portal
Publication:4651875
DOI10.1002/num.20006zbMath1067.65092OpenAlexW2121410213MaRDI QIDQ4651875
Raytcho D. Lazarov, Panagiotis Chatzipantelidis, Vidar Thomée
Publication date: 23 February 2005
Published in: Numerical Methods for Partial Differential Equations (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1002/num.20006
Finite difference methods for initial value and initial-boundary value problems involving PDEs (65M06) 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) Initial value problems for second-order parabolic equations (35K15) Method of lines for initial value and initial-boundary value problems involving PDEs (65M20)
Related Items (77)
Superconvergence analysis for a nonlinear parabolic equation with a BDF finite element method ⋮ A new error estimate for a primal-dual Crank-Nicolson mixed finite element using lowest degree Raviart-Thomas spaces for parabolic equations ⋮ A reduced-order extrapolation algorithm based on SFVE method and POD technique for non-stationary Stokes equations ⋮ The weak Galerkin method for solving the incompressible Brinkman flow ⋮ Cubic superconvergent finite volume element method for one-dimensional elliptic and parabolic equations ⋮ A two-grid method for finite volume element approximations of second-order nonlinear hyperbolic equations ⋮ Error estimates for finite volume element methods for convection--diffusion--reaction equations ⋮ Superconvergence analysis for nonlinear parabolic equation with \(EQ_1^{\mathrm{rot}}\) nonconforming finite element ⋮ A posteriori error estimate for finite volume element method of the second-order hyperbolic equations ⋮ A stabilized finite volume element method for a coupled Stokes-Darcy problem ⋮ An analysis of a second-order time accurate scheme for a finite volume method for parabolic equations on general nonconforming multidimensional spatial meshes ⋮ Two-grid methods for characteristic finite volume element solution of semilinear convection-diffusion equations ⋮ A finite volume spectral element method for solving magnetohydrodynamic (MHD) equations ⋮ 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 ⋮ Error estimates of Fourier finite volume element method for parabolic Dirichlet boundary optimal control problems on complex connected domains ⋮ Stability and Convergence of Stabilized Finite Volume Iterative Methods for Steady Incompressible MHD Flows with Different Viscosities ⋮ A posteriori error estimate for finite volume element method of the parabolic equations ⋮ Fully discrete heterogeneous multiscale method for parabolic problems with multiple spatial and temporal scales ⋮ Finite volume element methods for two-dimensional time fractional reaction–diffusion equations on triangular grids ⋮ On the semi-discrete stabilized finite volume method for the transient Navier-Stokes equations ⋮ Generalized difference simulation for coupled transport models of unsaturated soil water flow and solute ⋮ \(L^{2}\) error estimation of a quadratic finite volume element method for pseudo-parabolic equations in three spatial dimensions ⋮ A priori error estimates for finite volume element approximations to second order linear hyperbolic integro-differential equations ⋮ Some abstract error estimates of a finite volume scheme for a nonstationary heat equation on general nonconforming multidimensional spatial meshes. ⋮ A reduced FVE formulation based on POD method and error analysis for two-dimensional viscoelastic problem ⋮ A priori error estimates of finite volume element method for hyperbolic optimal control problems ⋮ Two-level stabilized finite volume methods for stationary Navier-Stokes equations ⋮ A stabilized multi-level method for non-singular finite volume solutions of the stationary 3D Navier-Stokes equations ⋮ Biquadratic finite volume element methods based on optimal stress points for parabolic problems ⋮ Weak Galerkin finite element method with second-order accuracy in time for parabolic problems ⋮ Finite Element Analysis in Fluid Mechanics ⋮ A reduced-order finite volume element formulation based on POD method and numerical simulation for two-dimensional solute transport problems ⋮ A two-grid method for the semi-linear reaction-diffusion system of the solutes in the groundwater flow by finite volume element ⋮ Finite volume element method and its stability analysis for analyzing the behavior of sub-diffusion problems ⋮ Proper orthogonal decomposition-based reduced-order stabilized mixed finite volume element extrapolating model for the nonstationary incompressible Boussinesq equations ⋮ A fully discrete stabilized mixed finite volume element formulation for the non-stationary conduction-convection problem ⋮ Weak Galerkin method with \((r, r - 1, r - 1)\)-order finite elements for second order parabolic equations ⋮ Finite volume element approximation for time dependent convection diffusion reaction equations with memory ⋮ Discontinuous finite volume element method for a coupled non-stationary Stokes-Darcy problem ⋮ Stable non-symmetric coupling of the finite volume method and the boundary element method for convection-dominated parabolic-elliptic interface problems ⋮ Two-Grid Finite Volume Element Method Combined with Crank-Nicolson Scheme for Semilinear Parabolic Equations ⋮ Unconditional superconvergence analysis for nonlinear parabolic equation with \(EQ_1^{rot}\) nonconforming finite element ⋮ Numerical analysis of a stable finite volume scheme for a generalized thermistor model ⋮ The Fourier finite element method for the corner singularity expansion of the heat equation ⋮ A POD-based reduced-order Crank-Nicolson finite volume element extrapolating algorithm for 2D Sobolev equations ⋮ Superconvergent biquadratic finite volume element method for two-dimensional Poisson's equations ⋮ Some error estimates of finite volume element method for parabolic optimal control problems ⋮ Two-grid finite volume element methods for semilinear parabolic problems ⋮ Error estimates of CFVE method for fully nonlinear convection-dominated diffusion problems ⋮ Biquadratic finite volume element method based on optimal stress points for second order hyperbolic equations ⋮ Discontinuous finite volume element method for parabolic problems ⋮ A finite volume element formulation and error analysis for the non-stationary conduction-convection problem ⋮ New finite volume element methods in the ALE framework for time-dependent convection-diffusion problems in moving domains ⋮ Finite Volume Methods for Elliptic PDE's: A New Approach ⋮ Error estimates for a non-local thermistor problem ⋮ A Crank-Nicolson finite volume element method for two-dimensional Sobolev equations ⋮ Two-grid Methods for Finite Volume Element Approximations of Nonlinear Sobolev Equations ⋮ Error analysis of a FVEM for fractional order evolution equations with nonsmooth initial data ⋮ Fourier Finite Volume Element Method for Two Classes of Optimal Control Problems Governed by Elliptic PDEs on Complex Connected Domain ⋮ Two new error estimates of a fully discrete primal-dual mixed finite element scheme for parabolic equations in any space dimension ⋮ Optimal estimates on stabilized finite volume methods for the incompressible Navier–Stokes model in three dimensions ⋮ Parabolic finite volume element equations in nonconvex polygonal domains ⋮ Two-grid methods for finite volume element approximations of nonlinear parabolic equations ⋮ A Priori Error Estimates of <scp>C</scp> rank–Nicolson Finite Volume Element Method for a Hyperbolic Optimal Control Problem ⋮ Postprocessing of a finite volume element method for semilinear parabolic problems ⋮ A postprocessing finite volume element method for time-dependent Stokes equations ⋮ ADI quadratic finite volume element methods for second order hyperbolic problems ⋮ Two-grid finite volume element method for the time-dependent Schrödinger equation ⋮ Some error estimates for the lumped mass finite element method for a parabolic problem ⋮ A Finite Volume Element Method for a Nonlinear Parabolic Problem ⋮ On the finite volume element method for self-adjoint parabolic integrodifferential equations ⋮ A two-grid characteristic finite volume element method for semilinear advection-dominated diffusion equations ⋮ Crank-Nicolson Method of a Two-Grid Finite Volume Element Algorithm for Nonlinear Parabolic Equations ⋮ Weak Galerkin finite element methods for Parabolic equations ⋮ Two-Grid Crank-Nicolson Finite Volume Element Method for the Time-Dependent Schrödinger Equation ⋮ Finite volume element method with the WSGD formula for nonlinear fractional mobile/immobile transport equations ⋮ A stabilized Crank-Nicolson mixed finite volume element formulation for the non-stationary incompressible Boussinesq equations
Cites Work
- On the finite volume element method
- Semigroups of linear operators and applications to partial differential equations
- Finite volume element methods for non-definite problems
- Some Error Estimates for the Box Method
- A Weak Discrete Maximum Principle and Stability of the Finite Element Method in L ∞ on Plane Polygonal Domains. I
- On the Analysis of Finite Volume Methods for Evolutionary Problems
- Finite Volume Methods for Elliptic PDE's: A New Approach
- Finite volume methods for convection-diffusion equations with right-hand side inH-1
- On the Accuracy of the Finite Volume Element Method Based on Piecewise Linear Polynomials
- Error estimates in $L^2$, $H^1$ and $L^\infty$ in covolume methods for elliptic and parabolic problems: A unified approach
- Finite volume element approximations of nonlocal reactive flows in porous media
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
This page was built for publication: Error estimates for a finite volume element method for parabolic equations in convex polygonal domains
