Comparison of two-dimensional \(r\)-adaptive finite element methods using various error indicators

DOI10.1016/S0378-4754(01)00285-3zbMath0984.65099WikidataQ126550727 ScholiaQ126550727MaRDI QIDQ5943293

Weizhang Huang, Robert D. Russell, Weiming Cao

Publication date: 12 May 2002

Published in: Mathematics and Computers in Simulation (Search for Journal in Brave)

zbMATH Keywords

numerical resultserror estimatesfinite element methodsmoving mesh

Mathematics Subject Classification ID

Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs (65M60) Error bounds for initial value and initial-boundary value problems involving PDEs (65M15) Mesh generation, refinement, and adaptive methods for the numerical solution of initial value and initial-boundary value problems involving PDEs (65M50)

Related Items (5)

A space-time adaptive method for reservoir flows: formulation and one-dimensional application ⋮ Adaptive mesh movements -- the MMPDE approach and its applications ⋮ A new anisotropic mesh adaptation method based upon hierarchical a posteriori error estimates ⋮ Practical aspects of formulation and solution of moving mesh partial differential equations ⋮ An \(hr\)-adaptive method for the cubic nonlinear Schrödinger equation

Cites Work

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• An \(r\)-adaptive finite element method based upon moving mesh PDEs
• A two-dimensional moving finite element method with local refinement based on a posteriori error estimates
• Mesh update strategies in parallel finite element computations of flow problems with moving boundaries and interfaces
• A Geometrical-Mechanical Interpretation of Gradient-Weighted Moving Finite Elements
• A Posteriori Error Estimates Based on Hierarchical Bases
• Some A Posteriori Error Estimators for Elliptic Partial Differential Equations
• A Moving Finite Element Method with Error Estimation and Refinement for One-Dimensional Time Dependent Partial Differential Equations
• Diagonally Implicit Runge–Kutta Methods for Stiff O.D.E.’s
• Moving Mesh Strategy Based on a Gradient Flow Equation for Two-Dimensional Problems
• A Study of Monitor Functions for Two-Dimensional Adaptive Mesh Generation
• Mesh Smoothing Using A Posteriori Error Estimates
• A moving grid finite‐element method using grid deformation

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