Adaptive finite element methods

Smoothness and regularity of solutions to PDEs (35B65) Spectral, collocation and related methods for boundary value problems involving PDEs (65N35) 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) Second-order elliptic equations (35J15) Mesh generation, refinement, and adaptive methods for boundary value problems involving PDEs (65N50)

Cites Work

The completion of locally refined simplicial partitions created by bisection
The Mathematical Theory of Finite Element Methods
A Unilaterally Constrained Quadratic Minimization with Adaptive Finite Elements
LOCALLY EFFICIENT AND RELIABLEA POSTERIORIERROR ESTIMATORS FOR DIRICHLET PROBLEMS
Adaptive VEM: Stabilization-Free A Posteriori Error Analysis and Contraction Property
Instance optimality of the adaptive maximum strategy
Guaranteed contraction of adaptive inexact hp-refinement strategies with realistic stopping criteria
Higher-order adaptive virtual element methods with contraction properties
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Approximating gradients with continuous piecewise polynomial functions
Axioms of adaptivity
High-order AFEM for the Laplace-Beltrami operator: convergence rates
An optimal Poincaré inequality for convex domains
The many proofs of an identity on the norm of oblique projections
A framework for obtaining guaranteed error bounds for finite element approximations
Equilibrated residual error estimates are $p$-robust
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
Two families of mixed finite elements for second order elliptic problems
Mixed finite elements in $\mathbb{R}^3$
Direct and inverse error estimates for finite elements with mesh refinements
A numerical solution of the Navier-Stokes equations using the finite element technique
An algorithm for adaptive mesh refinement in $n$ dimensions
Some observations on Babuška and Brezzi theories
Elliptic partial differential equations of second order
Discrete $p$-robust $\boldsymbol H(\mathrm{div})$-liftings and a posteriori estimates for elliptic problems with $H^{-1}$ source terms
Whitney estimates for convex domains with applications to multivariate piecewise polynomial approximation
Localization of the Aronszajn-Slobodeckij norm and application to adaptive boundary element methods. II: The three-dimensional case
Convergent adaptive finite elements for the nonlinear Laplacian
Fast computation in adaptive tree approximation
Adaptive finite element methods with convergence rates
The inhomogeneous Dirichlet problem in Lipschitz domains
Convergence rates of AFEM with $H^{-1}$ data
Convergence of adaptive finite element methods with error-dominated oscillation
Oscillation in a posteriori error estimation
Decay rates of adaptive finite elements with Dörfler marking
Efficient implementation of adaptive P1-FEM in Matlab
Optimality of a standard adaptive finite element method
Error-bounds for finite element method
Near-best adaptive approximation on conforming meshes
Pinching, Trimming, Truncating, and Averaging of Matrices
AFEM for Geometric PDE: The Laplace-Beltrami Operator
Primer of Adaptive Finite Element Methods
Mathematically Founded Design of Adaptive Finite Element Software
Efficient rectangular mixed finite elements in two and three space variables
Quasi-Optimal Convergence Rate of an Adaptive Discontinuous Galerkin Method
Quasioptimal cardinality of AFEM driven by nonresidual estimators
A posteriori error estimate for the mixed finite element method
Approximation classes for adaptive higher order finite element approximation
ENERGY NORM A POSTERIORI ERROR ESTIMATION OF hp-ADAPTIVE DISCONTINUOUS GALERKIN METHODS FOR ELLIPTIC PROBLEMS
Finite Element Interpolation of Nonsmooth Functions Satisfying Boundary Conditions
On the Marchaud-Type Inequality
A BASIC CONVERGENCE RESULT FOR CONFORMING ADAPTIVE FINITE ELEMENTS
Theory of adaptive finite element methods: An introduction
Optimal multilevel methods for H(grad), H(curl), and H(div) systems on graded and unstructured grids
Explicit Upper Bounds for Dual Norms of Residuals
Quasi-Optimal Convergence Rate for an Adaptive Finite Element Method
Interpolation of Besov Spaces
Lipschitz Continuity of Functions of Operators in the Schatten Classes
Polynomial Approximation of Functions in Sobolev Spaces
On the poisson equation with intersecting interfaces
Error Estimates for Adaptive Finite Element Computations
A Local Regularization Operator for Triangular and Quadrilateral Finite Elements
Local Bisection Refinement for N-Simplicial Grids Generated by Reflection
A comparison of adaptive refinement techniques for elliptic problems
Poincaré--Friedrichs Inequalities for Piecewise H¹ Functions
A Posteriori Error Estimators for Regularized Total Variation of Characteristic Functions
Localization of the Aronszajn-Slobodeckij norm and application to adaptive boundary elements methods. Part I. The two-dimensional case
Data Oscillation and Convergence of Adaptive FEM
Unified Analysis of Discontinuous Galerkin Methods for Elliptic Problems
Tree Approximation for hp-Adaptivity
A Local A Posteriori Error Estimator Based on Equilibrated Fluxes
An Adaptive Uzawa FEM for the Stokes Problem: Convergence without the Inf-Sup Condition
Convergence of Adaptive Finite Element Methods
Local problems on stars: A posteriori error estimators, convergence, and performance
The $hp$-local discontinuous Galerkin method for low-frequency time-harmonic Maxwell equations
A Convergent Adaptive Algorithm for Poisson’s Equation
A Posteriori Error Estimates for Elliptic Problems in Two and Three Space Dimensions
Mixed Finite Element Methods and Applications
Inf-sup stability implies quasi-orthogonality
Localization of the W-1,q norm for local a posteriori efficiency
DG approach to large bending plate deformations with isometry constraint
Optimality of a Standard Adaptive Finite Element Method for the Stokes Problem
Adaptive finite element methods for the Stokes problem with discontinuous viscosity
Finite Elemente
Convergence of Adaptive Discontinuous Galerkin Approximations of Second‐Order Elliptic Problems
Adaptive Finite Element Methods for Elliptic Problems with Discontinuous Coefficients

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