Adaptive finite element methods (Q6598416)

scientific article; zbMATH DE number 7906742

Language	Label	Description	Also known as
English	Adaptive finite element methods	scientific article; zbMATH DE number 7906742

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title

Adaptive finite element methods (English)

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5 September 2024

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zbMATH Keywords

adaptive finite element methods

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discontinuous Galerkin methods

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second-order elliptic PDEs

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A framework for obtaining guaranteed error bounds for finite element approximations

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A posteriori error estimation in finite element analysis

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Unified Analysis of Discontinuous Galerkin Methods for Elliptic Problems

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Error-bounds for finite element method

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Q5646339

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Q3214109

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A feedback finite element method with a posteriori error estimation. I: The finite element method and some basic properties of the a posteriori error estimator

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Error Estimates for Adaptive Finite Element Computations

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Direct and inverse error estimates for finite elements with mesh refinements

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An Adaptive Uzawa FEM for the Stokes Problem: Convergence without the Inf-Sup Condition

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Adaptive VEM: Stabilization-Free A Posteriori Error Analysis and Contraction Property

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Q4112938

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A Local Regularization Operator for Triangular and Quadrilateral Finite Elements

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Pinching, Trimming, Truncating, and Averaging of Matrices

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Tree Approximation for hp-Adaptivity

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Fast computation in adaptive tree approximation

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Adaptive finite element methods with convergence rates

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Q4439547

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Near-best adaptive approximation on conforming meshes

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Localization of the W-1,q norm for local a posteriori efficiency

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Mixed Finite Element Methods and Applications

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Adaptive finite element methods for the Stokes problem with discontinuous viscosity

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Quasi-Optimal Convergence Rate of an Adaptive Discontinuous Galerkin Method

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High-order AFEM for the Laplace-Beltrami operator: convergence rates

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AFEM for Geometric PDE: The Laplace-Beltrami Operator

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Adaptive Finite Element Methods for Elliptic Problems with Discontinuous Coefficients

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DG approach to large bending plate deformations with isometry constraint

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A Posteriori Error Estimates for Elliptic Problems in Two and Three Space Dimensions

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Finite Elemente

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Equilibrated residual error estimates are $p$-robust

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Poincaré--Friedrichs Inequalities for Piecewise H1 Functions

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The Mathematical Theory of Finite Element Methods

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Q4105995

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Two families of mixed finite elements for second order elliptic problems

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Efficient rectangular mixed finite elements in two and three space variables

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Q4500701

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Higher-order adaptive virtual element methods with contraction properties

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Q5524633

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A posteriori error estimate for the mixed finite element method

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Axioms of adaptivity

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Quasioptimal cardinality of AFEM driven by nonresidual estimators

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Quasi-Optimal Convergence Rate for an Adaptive Finite Element Method

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The finite element methods for elliptic problems.

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Q4144698

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Convergence rates of AFEM with $H^{-1}$ data

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Guaranteed contraction of adaptive inexact hp-refinement strategies with realistic stopping criteria

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Lipschitz Continuity of Functions of Operators in the Schatten Classes

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Whitney estimates for convex domains with applications to multivariate piecewise polynomial approximation

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Q4215356

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Q4273944

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Interpolation of Besov Spaces

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Instance optimality of the adaptive maximum strategy

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On the Marchaud-Type Inequality

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A Convergent Adaptive Algorithm for Poisson’s Equation

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Q5336643

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Polynomial Approximation of Functions in Sobolev Spaces

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Discrete $p$-robust $\boldsymbol H(\mathrm{div})$-liftings and a posteriori estimates for elliptic problems with $H^{-1}$ source terms

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Q5189317

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Localization of the Aronszajn-Slobodeckij norm and application to adaptive boundary elements methods. Part I. The two-dimensional case

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Localization of the Aronszajn-Slobodeckij norm and application to adaptive boundary element methods. II: The three-dimensional case

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Optimality of a Standard Adaptive Finite Element Method for the Stokes Problem

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Inf-sup stability implies quasi-orthogonality

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A Posteriori Error Estimators for Regularized Total Variation of Characteristic Functions

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Efficient implementation of adaptive P1-FEM in Matlab

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Q4292463

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Approximation classes for adaptive higher order finite element approximation

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Elliptic partial differential equations of second order

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ENERGY NORM A POSTERIORI ERROR ESTIMATION OF hp-ADAPTIVE DISCONTINUOUS GALERKIN METHODS FOR ELLIPTIC PROBLEMS

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The inhomogeneous Dirichlet problem in Lipschitz domains

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Q3280236

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Convergence of Adaptive Discontinuous Galerkin Approximations of Second‐Order Elliptic Problems

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On the poisson equation with intersecting interfaces

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Decay rates of adaptive finite elements with Dörfler marking

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Convergence of adaptive finite element methods with error-dominated oscillation

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Oscillation in a posteriori error estimation

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Q5832587

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Q5322841

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A Local A Posteriori Error Estimator Based on Equilibrated Fluxes

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Local Bisection Refinement for N-Simplicial Grids Generated by Reflection

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Q5334555

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A comparison of adaptive refinement techniques for elliptic problems

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Local problems on stars: A posteriori error estimators, convergence, and performance

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Data Oscillation and Convergence of Adaptive FEM

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Convergence of Adaptive Finite Element Methods

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A BASIC CONVERGENCE RESULT FOR CONFORMING ADAPTIVE FINITE ELEMENTS

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Mixed finite elements in $\mathbb{R}^3$

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Q5719600

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Primer of Adaptive Finite Element Methods

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Theory of adaptive finite element methods: An introduction

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An optimal Poincaré inequality for convex domains

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The $hp$-local discontinuous Galerkin method for low-frequency time-harmonic Maxwell equations

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Q4136469

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LOCALLY EFFICIENT AND RELIABLEA POSTERIORIERROR ESTIMATORS FOR DIRICHLET PROBLEMS

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Finite Element Interpolation of Nonsmooth Functions Satisfying Boundary Conditions

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A Unilaterally Constrained Quadratic Minimization with Adaptive Finite Elements

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Mathematically Founded Design of Adaptive Finite Element Software

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Optimality of a standard adaptive finite element method

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The completion of locally refined simplicial partitions created by bisection

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The many proofs of an identity on the norm of oblique projections

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A numerical solution of the Navier-Stokes equations using the finite element technique

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An algorithm for adaptive mesh refinement in $n$ dimensions

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Convergent adaptive finite elements for the nonlinear Laplacian

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Approximating gradients with continuous piecewise polynomial functions

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Explicit Upper Bounds for Dual Norms of Residuals

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Q4916237

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Some observations on Babuška and Brezzi theories

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Optimal multilevel methods for H(grad), H(curl), and H(div) systems on graded and unstructured grids

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Identifiers

Mathematics Subject Classification ID

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10.1017/S0962492924000011

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Sitelinks

Mathematics(1 entry)

mardi Publication:6598416