A family of interior-penalized weak Galerkin methods for second-order elliptic equations

DOI10.3934/math.2021030zbMath1484.65301OpenAlexW3093309200MaRDI QIDQ2131475

Kaifang Liu, Lun-Ji Song

Publication date: 26 April 2022

Published in: AIMS Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.3934/math.2021030

zbMATH Keywords

finite element methodssuperconvergencesecond-order elliptic equationinterior-penalized weak Galerkin

Mathematics Subject Classification ID

Error bounds for boundary value problems involving PDEs (65N15) Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs (65N30) Second-order elliptic equations (35J15)

Related Items

Three interior penalty DG methods for stationary incompressible magnetohydrodynamics ⋮ A stabilizer free weak Galerkin finite element method for parabolic equation

Uses Software

• Gmsh

Cites Work

• A locking-free weak Galerkin finite element method for elasticity problems in the primal formulation
• Weak Galerkin methods for second order elliptic interface problems
• Weak Galerkin finite element methods for Darcy flow: anisotropy and heterogeneity
• A weak Galerkin finite element method for the Maxwell equations
• Weak Galerkin methods for time-dependent Maxwell's equations
• A weak Galerkin finite element scheme with boundary continuity for second-order elliptic problems
• A new weak Galerkin finite element method for elliptic interface problems
• A weak Galerkin method with an over-relaxed stabilization for low regularity elliptic problems
• A relaxed weak Galerkin method for elliptic interface problems with low regularity
• Theory and practice of finite elements.
• A weak Galerkin finite element method for second-order elliptic problems
• New discretization schemes for time-harmonic Maxwell equations by weak Galerkin finite element methods
• A stabilizer-free weak Galerkin finite element method on polytopal meshes
• A weak Galerkin finite element method with polynomial reduction
• An efficient numerical scheme for the biharmonic equation by weak Galerkin finite element methods on polygonal or polyhedral meshes
• A modified weak Galerkin finite element method
• Weak Galerkin finite element methods for Parabolic equations
• A new weak Galerkin finite element method for the Helmholtz equation
• A weak Galerkin mixed finite element method for second order elliptic problems
• Weak Galerkin Finite Element Methods on Polytopal Meshes
• Discontinuous Galerkin Methods for Solving Elliptic and Parabolic Equations
• Gmsh: A 3-D finite element mesh generator with built-in pre- and post-processing facilities
• Supercloseness analysis and polynomial preserving Recovery for a class of weak Galerkin Methods
• A weak Galerkin mixed finite element method for the Helmholtz equation with large wave numbers
• Weak Galerkin method for the coupled Darcy–Stokes flow
• Mixed Finite Element Methods and Applications
• A Weak Galerkin Method with RT Elements for a Stochastic Parabolic Differential Equation
• A Weak Galerkin Method with $C^0$ Element for Forth Order Linear Parabolic Equation
• Numerical Approximation to A Stochastic Parabolic PDE with Weak Galerkin Method
• A Least-Squares-Based Weak Galerkin Finite Element Method for Second Order Elliptic Equations
• An Over-Penalized Weak Galerkin Method for Second-Order Elliptic Problems
• The Mathematical Theory of Finite Element Methods
• A weak Galerkin finite element method for the Stokes equations