A weak Galerkin method and its two‐grid algorithm for the quasi‐linear elliptic problems of non‐monotone type

DOI10.1002/num.22923arXiv2202.11164OpenAlexW4225907426WikidataQ115397143 ScholiaQ115397143MaRDI QIDQ6064508

Shenglan Xie, Peng Zhu

Publication date: 12 December 2023

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

Full work available at URL: https://arxiv.org/abs/2202.11164

zbMATH Keywords

finite element methodtwo-grid methodweak Galerkinquasi-linear elliptic problemnon-monotone type

Mathematics Subject Classification ID

Numerical analysis (65-XX) Partial differential equations (35-XX)

Cites Work

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• \texttt{PolyMesher}: a general-purpose mesh generator for polygonal elements written in Matlab
• Two-grid discontinuous Galerkin method for quasi-linear elliptic problems
• A \(C^0\)-weak Galerkin finite element method for the biharmonic equation
• A weak Galerkin finite element scheme for the biharmonic equations by using polynomials of reduced order
• Mathematical aspects of discontinuous Galerkin methods.
• Stabilizer-free weak Galerkin methods for monotone quasilinear elliptic PDEs
• A weak Galerkin finite element method for the Maxwell equations
• A new weak Galerkin finite element method for elliptic interface problems
• A weak Galerkin finite element method for second-order elliptic problems
• Weak-Galerkin finite element methods for a second-order elliptic variational inequality
• Weak Galerkin finite element method for a class of quasilinear elliptic problems
• A weak Galerkin finite element method for nonlinear conservation laws
• A stabilizer-free weak Galerkin finite element method on polytopal meshes
• Analysis on an HDG method for the \(p\)-Laplacian equations
• 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
• On L² Error Estimate for Weak Galerkin Finite Element Methods for Parabolic Problems
• 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 Finite Element Approximation of Nonlinear Second-Order Elliptic and Hyperbolic Systems
• Mixed Finite Element Methods for Quasilinear Second-Order Elliptic Problems
• A Galerkin Method for a Nonlinear Dirichlet Problem
• A Novel Two-Grid Method for Semilinear Elliptic Equations
• Poincaré--Friedrichs Inequalities for Piecewise H¹ Functions
• Two-Grid Discretization Techniques for Linear and Nonlinear PDE<scp>s</scp>
• Mixed Finite Element Methods for Nonlinear Second-Order Elliptic Problems
• A Stabilizer Free Weak Galerkin Method for the Biharmonic Equation on Polytopal Meshes
• Development of a P₂ element with optimal L² convergence for biharmonic equation
• Weak Galerkin finite element methods for the biharmonic equation on polytopal meshes
• An $hp$-local discontinuous Galerkin method for some quasilinear elliptic boundary value problems of nonmonotone type
• Discontinuous Galerkin Methods for Quasi‐Linear Elliptic Problems of Nonmonotone Type
• A Weak Galerkin Finite Element Method for Singularly Perturbed Convection-Diffusion--Reaction Problems