A \(C^0\)-weak Galerkin finite element method for the biharmonic equation

DOI10.1007/s10915-013-9770-4zbMath1305.65233arXiv1212.0250OpenAlexW2013146727WikidataQ62727793 ScholiaQ62727793MaRDI QIDQ474916

Xiu Ye, Junping Wang, Shangyou Zhang, Lin Mu

Publication date: 25 November 2014

Published in: Journal of Scientific Computing (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1212.0250

zbMATH Keywords

error estimatetriangular meshweak Laplaciantetrahedral meshbiharmonic problemsweak Galerkin finite element method

Mathematics Subject Classification ID

Boundary value problems for higher-order elliptic equations (35J40) Error bounds for boundary value problems involving PDEs (65N15) Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs (65N30)

Related Items (62)

A Stabilizer-Free Weak Galerkin Finite Element Method for the Stokes Equations ⋮ A weak Galerkin finite element scheme for solving the stationary Stokes equations ⋮ Semi-Discrete and Fully Discrete Weak Galerkin Finite Element Methods for a Quasistatic Maxwell Viscoelastic Model ⋮ A weak Galerkin generalized multiscale finite element method ⋮ Hybrid High-Order and Weak Galerkin Methods for the Biharmonic Problem ⋮ Hybridized weak Galerkin finite element method for linear elasticity problem in mixed form ⋮ The weak Galerkin method for solving the incompressible Brinkman flow ⋮ Convergence of an adaptive modified WG method for second-order elliptic problem ⋮ A staggered cell-centered DG method for the biharmonic Steklov problem on polygonal meshes: a priori and a posteriori analysis ⋮ A Mixed Finite Element Scheme for Biharmonic Equation with Variable Coefficient and von Kármán Equations ⋮ A Posteriori Error Estimates for a Modified Weak Galerkin Finite Element Approximation of Second Order Elliptic Problems with DG Norm ⋮ A weak Galerkin finite element scheme with boundary continuity for second-order elliptic problems ⋮ A Posteriori Error Estimates of Edge Residual-Type of Weak Galerkin Mixed FEM Solving Second-Order Elliptic Problems on Polytopal Mesh ⋮ Weak Galerkin finite element methods for the simulation of single-phase flow in fractured porous media ⋮ A family of H-div-div mixed triangular finite elements for the biharmonic equation ⋮ Weak Galerkin finite element method for linear elasticity interface problems ⋮ Four-order superconvergent weak Galerkin methods for the biharmonic equation on triangular meshes ⋮ A weak Galerkin method and its two‐grid algorithm for the quasi‐linear elliptic problems of non‐monotone type ⋮ A P₀–P₀ weak Galerkin finite element method for solving singularly perturbed reaction–diffusion problems ⋮ Convergence and optimality of an adaptive modified weak Galerkin finite element method ⋮ A modified weak Galerkin method for \(\boldsymbol{H}(\mathrm{curl})\)-elliptic problem ⋮ Four-order superconvergent CDG finite elements for the biharmonic equation on triangular meshes ⋮ Numerical analysis of energy stable weak Galerkin schemes for the Cahn-Hilliard equation ⋮ A Conforming Dg Method for the Biharmonic Equation on Polytopal Meshes ⋮ A primal-dual weak Galerkin finite element method for second order elliptic equations in non-divergence form ⋮ A stabilizer-free \(C^0\) weak Galerkin method for the biharmonic equations ⋮ A hybridized weak Galerkin finite element scheme for the Stokes equations ⋮ Supercloseness analysis and polynomial preserving Recovery for a class of weak Galerkin Methods ⋮ A Stabilizer Free Weak Galerkin Method for the Biharmonic Equation on Polytopal Meshes ⋮ A posteriori error estimates for weak Galerkin finite element methods for second order elliptic problems ⋮ A posteriori error estimates for weak Galerkin methods for second order elliptic problems on polygonal meshes ⋮ Weak Galerkin method for the Biot's consolidation model ⋮ A study of mixed problem for second order elliptic problems using modified weak Galerkin finite element method ⋮ A WEAK GALERKIN FINITE ELEMENT METHOD FOR THE SECOND ORDER ELLIPTIC PROBLEMS WITH MIXED BOUNDARY CONDITIONS ⋮ Coefficient Jump-Independent Approximation of the Conforming and Nonconforming Finite Element Solutions ⋮ A systematic study on weak Galerkin finite element methods for second order elliptic problems ⋮ A Weak Galerkin Method with $C^0$ Element for Forth Order Linear Parabolic Equation ⋮ The Weak Galerkin Method for Linear Hyperbolic Equation ⋮ A \(C^0\) weak Galerkin method for linear Cahn-Hilliard-cook equation with random initial condition ⋮ The Weak Galerkin Method for Elliptic Eigenvalue Problems ⋮ Weak Galerkin finite element method for a class of quasilinear elliptic problems ⋮ Lower and upper bounds of Laplacian eigenvalue problem by weak Galerkin method on triangular meshes ⋮ A curl-conforming weak Galerkin method for the quad-curl problem ⋮ A weak Galerkin finite element scheme for the Cahn-Hilliard equation ⋮ Convergence of adaptive weak Galerkin finite element methods for second order elliptic problems ⋮ A new \(P_1\) weak Galerkin method for the biharmonic equation ⋮ A new weak Galerkin finite element scheme for general second-order elliptic problems ⋮ A conforming discontinuous Galerkin finite element method on rectangular partitions ⋮ Hybridized weak Galerkin finite element methods for Brinkman equations ⋮ On the uniform convergence of the weak Galerkin finite element method for a singularly-perturbed biharmonic equation ⋮ AC⁰-weak Galerkin finite element method for fourth-order elliptic problems ⋮ A symmetric weak Galerkin method for solving non-divergence form elliptic equations ⋮ Conforming and nonconforming harmonic finite elements ⋮ A Primal-Dual Weak Galerkin Finite Element Method for Fokker--Planck Type Equations ⋮ Acceleration of weak Galerkin methods for the Laplacian eigenvalue problem ⋮ Polynomial preserving recovery for a class of weak Galerkin finite element methods ⋮ A modified weak Galerkin finite element method for nonmonotone quasilinear elliptic problems ⋮ An absolutely stable weak Galerkin finite element method for the Darcy-Stokes problem ⋮ A unified mortar condition for nonconforming finite elements ⋮ A WEAK GALERKIN METHOD FOR SECOND ORDER ELLIPTIC PROBLEMS WITH POLYNOMIAL REDUCTION ⋮ An over-penalized weak Galerkin method for parabolic interface problems with time-dependent coefficients ⋮ A Robust Modified Weak Galerkin Finite Element Method for Reaction-Diffusion Equations

Cites Work

• \(C^0\) interior penalty methods for fourth order elliptic boundary value problems on polygonal domains
• Mixed discontinuous Galerkin finite element method for the biharmonic equation
• \(hp\)-version a priori error analysis of interior penalty discontinuous Galerkin finite element approximations to the biharmonic equation
• A family of 3D continuously differentiable finite elements on tetrahedral grids
• Elliptic boundary value problems on corner domains. Smoothness and asymptotics of solutions
• The inhomogeneous Dirichlet problem for \(\Delta^2\) in Lipschitz domains
• Polynomial approximation on tetrahedrons in the finite element method
• Continuous/discontinuous finite element approximations of fourth-order elliptic problems in structural and continuum mechanics with applications to thin beams and plates, and strain gradient elasticity
• A weak Galerkin finite element method for second-order elliptic problems
• A computational study of the weak Galerkin method for second-order elliptic equations
• On the finite element method
• A Weak Galerkin Mixed Finite Element Method for Biharmonic Equations
• The Lowest Order Differentiable Finite Element on Rectangular Grids
• A weak Galerkin mixed finite element method for second order elliptic problems
• Finite Element Interpolation of Nonsmooth Functions Satisfying Boundary Conditions
• Mixed and nonconforming finite element methods : implementation, postprocessing and error estimates
• Finite Element Methods for Navier-Stokes Equations
• A Mixed Finite Element Method for the Biharmonic Equation
• A family of $C^1$ finite elements with optimal approximation properties for various Galerkin methods for 2nd and 4th order problems
• On the boundary value problem of the biharmonic operator on domains with angular corners
• On Cubic and Quartic Clough–Tocher Finite Elements
• Piecewise Quadratic Approximations on Triangles
• Approximation of the Biharmonic Equation by a Mixed Finite Element Method
• On the Full C₁-Q_k Finite Element Spaces on Rectangles and Cuboids
• The Best L² Norm Error Estimate of Lower Order Finite Element Methods for the Fourth Order Problem
• Weak Galerkin finite element methods for the biharmonic equation on polytopal meshes
• The Mathematical Theory of Finite Element Methods
• A C1-P2 finite element without nodal basis

This page was built for publication: A \(C^0\)-weak Galerkin finite element method for the biharmonic equation