Analysis of Adaptive Two-Grid Finite Element Algorithms for Linear and Nonlinear Problems

DOI10.1137/19M1285615zbMath1475.65214arXiv1805.07887MaRDI QIDQ5857732

Yi Zhang, Yukun Li

Publication date: 7 April 2021

Published in: SIAM Journal on Scientific Computing (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1805.07887

zbMATH Keywords

convergencereliabilityefficiencyadaptive algorithmsresidual-type a posteriori error estimatorstwo-grid finite element algorithms

Mathematics Subject Classification ID

Multigrid methods; domain decomposition for boundary value problems involving PDEs (65N55) Error bounds for boundary value problems involving PDEs (65N15) Stability and convergence of numerical methods for boundary value problems involving PDEs (65N12) Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs (65N30) Mesh generation, refinement, and adaptive methods for boundary value problems involving PDEs (65N50) Numerical solution of discretized equations for boundary value problems involving PDEs (65N22)

Related Items

Analysis of a goal-oriented adaptive two-grid finite-element algorithm for semilinear elliptic problems, A posteriori error estimates of two-grid weak Galerkin methods for semilinear elliptic differential equations, Convergence of adaptive two-grid weak Galerkin finite element methods for semilinear elliptic differential equations

Cites Work

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• Two-grid \(hp\)-version discontinuous Galerkin finite element methods for second-order quasilinear elliptic PDEs
• A posteriori error estimates of two-grid finite element methods for nonlinear elliptic problems
• Adaptive finite element methods with convergence rates
• On the stability and accuracy of partially and fully implicit schemes for phase field modeling
• Convergence and optimality of the adaptive nonconforming linear element method for the Stokes problem
• hp–Adaptive Two-Grid Discontinuous Galerkin Finite Element Methods for Quasi-Newtonian Fluid Flows
• Two–grid ℎ𝑝–DGFEM for second order quasilinear elliptic PDEs based on an incomplete Newton iteration
• Numerical Solution to a Mixed Navier–Stokes/Darcy Model by the Two-Grid Approach
• Analysis of symmetric interior penalty discontinuous Galerkin methods for the Allen–Cahn equation and the mean curvature flow
• Finite Element Interpolation of Nonsmooth Functions Satisfying Boundary Conditions
• A Two-Grid Method of a Mixed Stokes–Darcy Model for Coupling Fluid Flow with Porous Media Flow
• Quasi-Optimal Convergence Rate for an Adaptive Finite Element Method
• Iterative Methods by Space Decomposition and Subspace Correction
• A Novel Two-Grid Method for Semilinear Elliptic Equations
• A Posteriori Error Estimates for a Discontinuous Galerkin Approximation of Second-Order Elliptic Problems
• Data Oscillation and Convergence of Adaptive FEM
• A two-grid discretization scheme for eigenvalue problems
• Two-Grid Discretization Techniques for Linear and Nonlinear PDE<scp>s</scp>
• Convergence of Adaptive Finite Element Methods
• Error Estimates on a New Nonlinear Galerkin Method Based on Two-Grid Finite Elements
• A Convergent Adaptive Algorithm for Poisson’s Equation
• Convergence of Adaptive Discontinuous Galerkin Approximations of Second‐Order Elliptic Problems
• Two‐grid methods for time‐harmonic Maxwell equations