On the Accuracy of the Finite Volume Element Method Based on Piecewise Linear Polynomials

From MaRDI portal
Publication:4539397

DOI10.1137/S0036142900368873zbMath1036.65084OpenAlexW2023963475MaRDI QIDQ4539397

Tao Lin, Richard E. Ewing, Yan Ping Lin

Publication date: 8 July 2002

Published in: SIAM Journal on Numerical Analysis (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1137/s0036142900368873



Related Items

A discontinuous finite volume element method for second-order elliptic problems, A second-order finite volume element method on quadrilateral meshes for elliptic equations, Multilevel preconditioning for the finite volume method, The finite volume method based on stabilized finite element for the stationary Navier-Stokes problem, The hybrid Wilson finite volume method for elliptic problems on quadrilateral meshes, A mixed and discontinuous Galerkin finite volume element method for incompressible miscible displacement problems in porous media, Analysis of two-scale finite volume element method for elliptic problem, Analysis of three stabilized finite volume iterative methods for the steady Navier–Stokes equations, Finite volume element method with Lagrangian cubic functions, Upwind finite volume element methods for one-dimensional semiconductor device, A Discontinuous Finite Volume Element Method Based on Bilinear Trial Functions, $L^2$ Error Estimates for a Class of Any Order Finite Volume Schemes Over Quadrilateral Meshes, Is 2k-Conjecture Valid for Finite Volume Methods?, Unnamed Item, Construction and analysis of the quadratic finite volume methods on tetrahedral meshes, Unnamed Item, Finite volume element approximation for nonlinear diffusion problems with degenerate diffusion coefficients, Three dimensional high order finite volume element schemes for elliptic equations, Two‐level stabilized finite volume method for the stationary incompressible magnetohydrodynamic equations, Error estimates of Fourier finite volume element method for parabolic Dirichlet boundary optimal control problems on complex connected domains, A Coercivity Result of Quadratic Finite Volume Element Schemes over Triangular Meshes, Stability and Convergence of Stabilized Finite Volume Iterative Methods for Steady Incompressible MHD Flows with Different Viscosities, New Superconvergent Structures with Optional Superconvergent Points for the Finite Volume Element Method, A posteriori error estimate for finite volume element method of the parabolic equations, Unnamed Item, Adaptive parallel average Schwarz preconditioner for Crouzeix-Raviart finite volume method, Enhanced positive vertex-centered finite volume scheme for anisotropic convection-diffusion equations, A Finite Volume Element Solution Based on Postprocessing Technique Over Arbitrary Convex Polygonal Meshes, An unconditionally stable and \(L^2\) optimal quadratic finite volume scheme over triangular meshes for anisotropic elliptic equations, Discrete duality finite volume scheme for a generalized Joule heating problem, Unconditional stability and convergence analysis of fully discrete stabilized finite volume method for the time-dependent incompressible MHD flow, A polygonal finite volume element method for anisotropic diffusion problems, \(L^2\) error estimates for a family of cubic finite volume methods on triangular meshes, On pointwise error estimates for Voronoï-based finite volume methods for the Poisson equation on the sphere, The Hermite finite volume method with global conservation law, Numerical analysis of a Picard multilevel stabilization of mixed finite volume method for the 2D/3D incompressible flow with large data, A priori error estimates for finite volume element approximations to second order linear hyperbolic integro-differential equations, Optimal \(L^2\), \(H^1\) and \(L^{\infty}\) analysis of finite volume methods for the stationary Navier-Stokes equations with large data, Convergence Analysis of Discontinuous Finite Volume Methods for Elliptic Optimal Control Problems, Admissible Regions for Higher-Order Finite Volume Method Grids, A finite difference/finite volume method for solving the fractional diffusion wave equation, Finite volume element approximation for time dependent convection diffusion reaction equations with memory, Two-grid finite volume element method for linear and nonlinear elliptic problems, A full discrete two-grid finite-volume method for a nonlinear parabolic problem, A Quadratic Triangular Finite Volume Element Method for a Semilinear Elliptic Equation, Conservation Laws for Free-Boundary Fluid Layers, A Posteriori Error Analysis of Any Order Finite Volume Methods for Elliptic Problems, A Two-Grid Finite-Volume Method for the Schrodinger Equation, Two-Grid Finite Volume Element Method Combined with Crank-Nicolson Scheme for Semilinear Parabolic Equations, Finite volume element approximation of the coupled continuum pipe‐flow/Darcy model for flows in karst aquifers, Analysis of second order finite volume element methods for pseudo-parabolic equations in three spatial dimensions, Error estimates for a finite volume element method for parabolic equations in convex polygonal domains, Multiscale enrichment of a finite volume element method for the stationary Navier–Stokes problem, Finite volume schemes for diffusion equations: Introduction to and review of modern methods, Some error estimates of finite volume element method for parabolic optimal control problems, Adaptive Vertex-Centered Finite Volume Methods with Convergence Rates, A class of finite volume schemes of arbitrary order on nonuniform meshes, Biquadratic finite volume element method based on optimal stress points for second order hyperbolic equations, Discontinuous finite volume element method for parabolic problems, Finite volume method for the variational inequalities of first and second kinds, A mixed finite element method for nearly incompressible elasticity and Stokes equations using primal and dual meshes with quadrilateral and hexahedral grids, Analysis of a \(p\)-version finite volume method for 1D elliptic problems, Higher-order finite volume methods. II: Inf-sup condition and uniform local ellipticity, Error estimates of finite volume element method for the pollution in groundwater flow, Two-grid Methods for Finite Volume Element Approximations of Nonlinear Sobolev Equations, Fourier Finite Volume Element Method for Two Classes of Optimal Control Problems Governed by Elliptic PDEs on Complex Connected Domain, Optimal estimates on stabilized finite volume methods for the incompressible Navier–Stokes model in three dimensions, Two‐grid covolume schemes for elliptic problems, A posteriori error analysis of nonconforming finite volume elements for general second-order elliptic PDEs, Unnamed Item, A MODIFIED IMMERSED FINITE VOLUME ELEMENT METHOD FOR ELLIPTIC INTERFACE PROBLEMS, A Priori Error Estimates of <scp>C</scp> rank–Nicolson Finite Volume Element Method for a Hyperbolic Optimal Control Problem, $L^2$ Error Estimates for High Order Finite Volume Methods on Triangular Meshes, Conditioning of the finite volume element method for diffusion problems with general simplicial meshes, Superconvergence of finite volume methods for the Stokes equations, Discontinuous Galerkin finite volume element methods for second-order linear elliptic problems, Postprocessing of a finite volume element method for semilinear parabolic problems, A mixed finite element method for non-linear and nearly incompressible elasticity based on biorthogonal systems, Interior Estimates of Finite Volume Element Methods Over Quadrilateral Meshes for Elliptic Equations, A Characteristic Finite Volume Element Method for the Air Pollution Model, A construction of higher-order finite volume methods, Finite volume element method for monotone nonlinear elliptic problems, Error estimates for two-level penalty finite volume method for the stationary Navier-Stokes equations, Quadratic finite volume element method for the improved Boussinesq equation, Unnamed Item, 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, New superconvergent structures developed from the finite volume element method in 1D, A priori and posteriori error estimates of Legendre Galerkin spectral methods for general elliptic optimal control problems, Analysis of newton multilevel stabilized finite volume method for the three-dimensional stationary Navier-Stokes equations, ON VERTEX RECONSTRUCTIONS FOR CELL-CENTERED FINITE VOLUME APPROXIMATIONS OF 2D ANISOTROPIC DIFFUSION PROBLEMS, Two-Grid Crank-Nicolson Finite Volume Element Method for the Time-Dependent Schrödinger Equation, Superconvergence and gradient recovery for a finite volume element method for solving convection‐diffusion equations, The Corrected Finite Volume Element Methods for Diffusion Equations Satisfying Discrete Extremum Principle, An efficient symmetric finite volume element method for second-order variable coefficient parabolic integro-differential equations, Error estimates in \(L^2\) and \(L^\infty\) norms of finite volume method for the bilinear elliptic optimal control problem, A finite volume scheme with preconditioned Lanczos method for two-dimensional space-fractional reaction-diffusion equations, A sparse grid stochastic collocation upwind finite volume element method for the constrained optimal control problem governed by random convection diffusion equations, \(H^1\)-super-convergence of center finite difference method based on \(P_1\)-element for the elliptic equation, Additive average Schwarz method for a Crouzeix-Raviart finite volume element discretization of elliptic problems with heterogeneous coefficients, A two-grid method for finite volume element approximations of second-order nonlinear hyperbolic equations, A residual-type a posteriori error estimate of finite volume element method for a quasi-linear elliptic problem, Modeling and simulation of mixture flows: application to powder-snow avalanches, Additive Schwarz preconditioner for the finite volume element discretization of symmetric elliptic problems, Error estimates for finite volume element methods for convection--diffusion--reaction equations, On the accuracy of the mortar finite volume element method with Lagrange multipliers, Stability and convergence of spatial discrete stabilized finite volume method for the unsteady incompressible magnetohydrodynamics equations, Uniform convergence of finite volume element method with Crouzeix-Raviart element for non-self-adjoint and indefinite elliptic problems, A posteriori error estimate for finite volume element method of the second-order hyperbolic equations, A new high order finite volume element solution on arbitrary triangular and quadrilateral meshes, Superconvergence of any order finite volume schemes for 1D general elliptic equations, A generalization of the vertex-centered finite volume scheme to arbitrary high order, Two-grid methods for characteristic finite volume element solution of semilinear convection-diffusion equations, Conservative finite volume element schemes for the complex modified Korteweg-de Vries equation, The locally stabilized finite volume method for incompressible flow, Convergence analysis and numerical simulation for a hyperbolic system, A finite volume spectral element method for solving magnetohydrodynamic (MHD) equations, Vertex-centered finite volume schemes of any order over quadrilateral meshes for elliptic boundary value problems, Convergence and stability of a stabilized finite volume method for the stationary Navier-Stokes equations, Superconvergence of immersed finite volume methods for one-dimensional interface problems, Equal order discontinuous finite volume element methods for the Stokes problem, A stabilized finite volume method for Stokes equations using the lowest order \(P_1-P_0\) element pair, A unified analysis of a class of quadratic finite volume element schemes on triangular meshes, On the semi-discrete stabilized finite volume method for the transient Navier-Stokes equations, Analysis of a finite volume element method for the Stokes problem, A finite volume method for Stokes problems on quadrilateral meshes, A finite volume method for solving Navier-Stokes problems, Convergence of the discontinuous finite volume method for elliptic problems with minimal regularity, The optimal \(L^2\) error estimate of stabilized finite volume method for the stationary Navier-Stokes problem, A stabilized low order finite-volume method for the three-dimensional stationary Navier-Stokes equations, 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, Superconvergence of finite volume element method for elliptic problems, Modified method of characteristics combined with finite volume element methods for incompressible miscible displacement problems in porous media, Local superconvergence of post-processed high-order finite volume element solutions, A family of finite volume schemes of arbitrary order on rectangular meshes, A symmetric characteristic finite volume element scheme for nonlinear convection-diffusion problems, The MMOC and MMOCAA schemes for the finite volume element method of convection-diffusion problems, Rational Krylov methods for functions of matrices with applications to fractional partial differential equations, Nonconforming cell boundary element methods for elliptic problems on triangular mesh, Superconvergence of mixed covolume method for elliptic problems on triangular grids, From the Hu-Washizu formulation to the average nodal strain formulation, Some recent advances on vertex centered finite volume element methods for elliptic equations, The finite volume element method on the Shishkin mesh for a singularly perturbed reaction-diffusion problem, A posteriori error estimates of two-grid finite volume element methods for nonlinear elliptic 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 method for solving the stochastic Helmholtz equation, Error bounds for discontinuous finite volume discretisations of Brinkman optimal control problems, A diffuse interface box method for elliptic problems, The gradient superconvergence of the finite volume method for a nonlinear elliptic problem of nonmonotone type., A family of quadratic finite volume element schemes for anisotropic diffusion problems on triangular meshes, Stable non-symmetric coupling of the finite volume method and the boundary element method for convection-dominated parabolic-elliptic interface problems, A penalty finite volume method for the transient Navier-Stokes equations, Mortar finite volume element method with Crouzeix-Raviart element for parabolic problems, An unconditionally stable quadratic finite volume scheme over triangular meshes for elliptic equations, A non-symmetric coupling of the finite volume method and the boundary element method, Numerical analysis of a stable finite volume scheme for a generalized thermistor model, A two-level finite volume method for the unsteady Navier-Stokes equations based on two local Gauss integrations, Bilinear immersed finite volume element method for solving matrix coefficient elliptic interface problems with non-homogeneous jump conditions, A stabilized finite volume method for the stationary Navier-Stokes equations, Superconvergence of quadratic finite volume method on triangular meshes, The finite difference/finite volume method for solving the fractional diffusion equation, \(L^{2}\) error estimates and superconvergence of the finite volume element methods on quadrilateral meshes, Higher-order finite volume methods for elliptic boundary value problems, A new finite element method for Darcy-Stokes-Brinkman equations, An immersed finite volume element method for 2D PDEs with discontinuous coefficients and non-homogeneous jump conditions, Two-grid finite volume element methods for semilinear parabolic problems, Hierarchical error estimates for finite volume approximation solution of elliptic equations, The semidiscrete finite volume element method for nonlinear convection-diffusion problem, An algorithm using the finite volume element method and its splitting extrapolation, A posteriori error estimates for finite volume method based on bilinear trial functions for the elliptic equation, Finite volume element approximation and analysis for a kind of semiconductor device simulation, \(L^{2}\) error estimate of the finite volume element methods on quadrilateral meshes, High order locally conservative finite element solutions for anisotropic diffusion problems in two dimensions, Coercivity results of a modified \(Q_1\)-finite volume element scheme for anisotropic diffusion problems, Analysis of linear and quadratic simplicial finite volume methods for elliptic equations, Convergence analysis of an upwind finite volume element method with crouzeix-raviart element for non-selfadjoint and indefinite problems, A \(Q_1\)-finite volume element scheme for anisotropic diffusion problems on general convex quadrilateral mesh, A new stabilized finite volume method for the stationary Stokes equations, A finite volume method on general surfaces and its error estimates, Two-grid methods for finite volume element approximations of nonlinear parabolic equations, A family of quadratic finite volume element schemes over triangular meshes for elliptic equations, Numerical study of the unsteady 2D coupled magneto-hydrodynamic equations on regular/irregular pipe using direct meshless local Petrov-Galerkin method, Error estimation of a quadratic finite volume method on right quadrangular prism grids, Optimal weighted upwind finite volume method for convection-diffusion equations in 2D, Construction of locally conservative fluxes for high order continuous Galerkin finite element methods, Simplified weak Galerkin and new finite difference schemes for the Stokes equation, A postprocessing finite volume element method for time-dependent Stokes equations, Superconvergence of finite volume methods for the second-order elliptic problem, Error estimates of finite volume method for Stokes optimal control problem, Two-grid finite volume element method for the time-dependent Schrödinger equation, Finite volume element methods for a multi-dimensional fracture model, Unified construction and \(L^2\) analysis for the finite volume element method over tensorial meshes