The completion of locally refined simplicial partitions created by bisection
From MaRDI portal
Publication:5429498
DOI10.1090/S0025-5718-07-01959-XzbMath1131.65095OpenAlexW2044959876MaRDI QIDQ5429498
Publication date: 30 November 2007
Published in: Mathematics of Computation (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1090/s0025-5718-07-01959-x
adaptive mesh refinementadaptive finite element methodsbisection\(n\)-simplicesconforming partitions
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)
Related Items
Adaptive Finite Element Approximations for Elliptic Problems using Regularized Forcing Data, Adaptive VEM: Stabilization-Free A Posteriori Error Analysis and Contraction Property, An optimal adaptive mixed finite element method, Error Estimation and Adaptivity for Stochastic Collocation Finite Elements Part I: Single-Level Approximation, A convergent adaptive stochastic Galerkin finite element method with quasi-optimal spatial meshes, Adaptive Least-Squares, Discontinuous Petrov-Galerkin, and Hybrid High-Order Methods, Mathematically Founded Design of Adaptive Finite Element Software, Convergence and Optimality of Higher-Order Adaptive Finite Element Methods for Eigenvalue Clusters, Approximation classes for adaptive higher order finite element approximation, A Weak Compatibility Condition for Newest Vertex Bisection in Any Dimension, Adaptive BEM for elliptic PDE systems, part I: abstract framework, for weakly-singular integral equations, Red–green refinement of simplicial meshes in $d$ dimensions, A Multilevel Correction Type of Adaptive Finite Element Method for Eigenvalue Problems, Adaptive FEM for Parameter-Errors in Elliptic Linear-Quadratic Parameter Estimation Problems, Inf-sup stability implies quasi-orthogonality, Adaptive Nonintrusive Reconstruction of Solutions to High-Dimensional Parametric PDEs, Cost-optimal adaptive iterative linearized FEM for semilinear elliptic PDEs, Axioms of Adaptivity with Separate Marking for Data Resolution, Plain convergence of goal-oriented adaptive FEM, Analysis of an Adaptive Finite Element Method for Recovering the Robin Coefficient, Adaptive IGAFEM with optimal convergence rates: Hierarchical B-splines, Two-level error estimation for the integral fractional Laplacian, Adaptive finite element approximation of optimal control problems with the integral fractional Laplacian, A priori and a posteriori error analysis for semilinear problems in liquid crystals, Fractional elliptic problems on Lipschitz domains: regularity and approximation, Adaptive guaranteed lower eigenvalue bounds with optimal convergence rates, Improved rates for a space-time FOSLS of parabolic PDEs, Rational-approximation-based model order reduction of Helmholtz frequency response problems with adaptive finite element snapshots, An Adaptive Least-Squares FEM for Linear Elasticity with Optimal Convergence Rates, Optimal convergence of adaptive FEM for eigenvalue clusters in mixed form, Adaptive Finite Element Method for the Maxwell Eigenvalue Problem, Mixed Finite Element Approximation of the Hamilton--Jacobi--Bellman Equation with Cordes Coefficients, Convergence and optimality of adaptive edge finite element methods for time-harmonic Maxwell equations, Best approximation property in the $W^1_{\infty }$ norm for finite element methods on graded meshes, Quasi-optimal adaptive mixed finite element methods for controlling natural norm errors, Optimal Convergence Rates for Adaptive Lowest-Order Discontinuous Petrov--Galerkin Schemes, Convergence and Quasi-Optimality of an Adaptive Continuous Interior Penalty Finite Element Method, On the Sobolev and $L^p$-Stability of the $L^2$-Projection, Two-Level a Posteriori Error Estimation for Adaptive Multilevel Stochastic Galerkin Finite Element Method, Quasi-optimal adaptive hybridized mixed finite element methods for linear elasticity, A New Discretization for $m$th-Laplace Equations with Arbitrary Polynomial Degrees, Adaptive Vertex-Centered Finite Volume Methods with Convergence Rates, Adaptive nonconforming Crouzeix-Raviart FEM for eigenvalue problems, Convergence and optimality of adaptive mixed finite element methods, Adaptive isogeometric methods with hierarchical splines: Error estimator and convergence, Contraction property of adaptive hybridizable discontinuous Galerkin methods, Instance optimality of the adaptive maximum strategy, A posteriori error estimators for hierarchical B-spline discretizations, An Abstract Analysis of Optimal Goal-Oriented Adaptivity, Quasi-optimality of an Adaptive Finite Element Method for Cathodic Protection, A Cascadic Adaptive Finite Element Method for Nonlinear Eigenvalue Problems in Quantum Physics, A modified bubble placement method and its application in solving elliptic problem with discontinuous coefficients adaptively, Adaptive finite element approximation of steady flows of incompressible fluids with implicit power-law-like rheology, High-Order Adaptive Galerkin Methods, Optimality of a Standard Adaptive Finite Element Method for the Stokes Problem, Some Convergence and Optimality Results of Adaptive Mixed Methods in Finite Element Exterior Calculus, Adaptive Mixed Finite Element Methods for Non-self-adjoint Indefinite Second-Order Elliptic PDEs with Optimal Rates, Collective marking for adaptive least-squares finite element methods with optimal rates, Convergence of Adaptive Stochastic Galerkin FEM, Unstabilized Hybrid High-order Method for a Class of Degenerate Convex Minimization Problems, Quasi-optimal convergence rate for an adaptive method for the integral fractional Laplacian, The Prager–Synge theorem in reconstruction based a posteriori error estimation, Analysis of an adaptive Uzawa finite element method for the nonlinear Stokes problem, Rate optimality of adaptive finite element methods with respect to overall computational costs, Convergence of an adaptive finite element method for distributed flux reconstruction, Comparison Results of NonstandardP2Finite Element Methods for the Biharmonic Problem, Adaptive Finite Element Approximations for Kohn--Sham Models, Quasi‐optimality of the adaptive finite element method for the eigenvalue problem arising from the vibration frequencies of the cavity flow, Further results on a space-time FOSLS formulation of parabolic PDEs, On the stability of Scott-Zhang type operators and application to multilevel preconditioning in fractional diffusion, Space-Time Finite Element Discretization of Parabolic Optimal Control Problems with Energy Regularization, Adaptive Morley FEM for the von Kármán Equations with Optimal Convergence Rates, Multilevel decompositions and norms for negative order Sobolev spaces, Adaptive finite element methods for the Stokes problem with discontinuous viscosity, Anisotropic mesh adaptation for steady convection-dominated problems based on bubble-type local mesh generation, Convergence and quasi-optimality of an adaptive continuous interior multi-penalty finite element method, A wavelet-in-time, finite element-in-space adaptive method for parabolic evolution equations, Quasi-optimal complexity of adaptive finite element method for linear elasticity problems in two dimensions, An adaptive FEM for a Maxwell interface problem, Approximating gradients with continuous piecewise polynomial functions, Justification of the saturation assumption, Quasi-optimality of adaptive finite element methods for controlling local energy errors, Adaptive boundary element methods with convergence rates, Axioms of adaptivity, Goal-oriented a posteriori error estimation for the biharmonic problem based on an equilibrated moment tensor, Rate-optimal goal-oriented adaptive FEM for semilinear elliptic PDEs, Adaptive boundary element methods. A posteriori error estimators, adaptivity, convergence, and implementation, Nonlinear discontinuous Petrov-Galerkin methods, Convergence and optimality of the adaptive nonconforming linear element method for the Stokes problem, A discrete Helmholtz decomposition with morley finite element functions and the optimality of adaptive finite element schemes, Quasi-optimal convergence rate for an adaptive hybridizable \(C^0\) discontinuous Galerkin method for Kirchhoff plates, Classical FEM-BEM coupling methods: nonlinearities, well-posedness, and adaptivity, Unsymmetric multi-level hanging nodes and anisotropic polynomial degrees in \(H^1\)-conforming higher-order finite element methods, \(h\)-adaptive least-squares finite element methods for the 2D Stokes equations of any order with optimal convergence rates, Convergence and quasi-optimal cost of adaptive algorithms for nonlinear operators including iterative linearization and algebraic solver, Convergence and quasi-optimality of adaptive finite element methods for harmonic forms, Convergence rates of adaptive methods, Besov spaces, and multilevel approximation, On 2D newest vertex bisection: optimality of mesh-closure and \(H ^{1}\)-stability of \(L _{2}\)-projection, Convergent adaptive hybrid higher-order schemes for convex minimization, Optimal multilevel adaptive FEM for the Argyris element, Convergence and complexity of arbitrary order adaptive mixed element methods for the Poisson equation, Goal-oriented adaptive finite element methods with optimal computational complexity, Adaptive FEM for Helmholtz equation with large wavenumber, Convergence of an adaptive Kačanov FEM for quasi-linear problems, Optimal adaptive nonconforming FEM for the Stokes problem, Convergence and quasi-optimality of an adaptive finite element method for controlling \(L_{2}\) errors, Convergence and quasi-optimality of an adaptive finite element method for elliptic Robin boundary control problem, Convergence of adaptive BEM for some mixed boundary value problem, Error reduction of the adaptive conforming and nonconforming finite element methods with red-green refinement, Estimator reduction and convergence of adaptive BEM, A remark on the optimality of adaptive finite element methods, Decay rates of adaptive finite elements with Dörfler marking, How to prove optimal convergence rates for adaptive least-squares finite element methods, Convergence and optimality of the adaptive Morley element method, MooAFEM: an object oriented Matlab code for higher-order adaptive FEM for (nonlinear) elliptic PDEs, Near-best adaptive approximation on conforming meshes, Constructive approximation on graded meshes for the integral fractional Laplacian, A short note on plain convergence of adaptive least-squares finite element methods, On global and local mesh refinements by a generalized conforming bisection algorithm, Adaptive mesh refinement in 2D -- an efficient implementation in \textsc{Matlab}, T-IFISS: a toolbox for adaptive FEM computation, Goal-adaptive isogeometric analysis with hierarchical splines, Finite element approximations of nonlinear eigenvalue problems in quantum physics, ZZ-type a posteriori error estimators for adaptive boundary element methods on a curve, Quasi-optimal convergence rate of an adaptive weakly over-penalized interior penalty method, Goal-oriented error estimation and adaptivity for fluid-structure interaction using exact linearized adjoints, Optimal multilevel methods for graded bisection grids, Superconvergence in a DPG method for an ultra-weak formulation, Adaptive finite element analysis of elliptic problems based on bubble-type local mesh generation, Adaptive BEM with inexact PCG solver yields almost optimal computational costs, Multilevel correction adaptive finite element method for semilinear elliptic equation., Hierarchical Argyris finite element method for adaptive and multigrid algorithms, A convergent adaptive finite element method for cathodic protection, High-order AFEM for the Laplace-Beltrami operator: convergence rates, Goal-oriented error estimation and adaptivity for elliptic PDEs with parametric or uncertain inputs, Adaptive BEM with optimal convergence rates for the Helmholtz equation, Optimal adaptivity for the SUPG finite element method, An adaptive least-squares FEM for the Stokes equations with optimal convergence rates, Constants in discrete Poincaré and Friedrichs inequalities and discrete quasi-interpolation, Partial relaxation of \(C^0\) vertex continuity of stresses of conforming mixed finite elements for the elasticity problem, Instance-optimal goal-oriented adaptivity, Error analysis of Nitsche's and discontinuous Galerkin methods of a reduced Landau-de Gennes problem, Adaptive finite element method for elliptic optimal control problems: convergence and optimality, Convergence and optimal complexity of adaptive finite element eigenvalue computations, Convergence and quasi-optimality of adaptive FEM with inhomogeneous Dirichlet data, A linear Uzawa-type FEM-BEM solver for nonlinear transmission problems, An adaptive mesh refinement strategy for finite element solution of the elliptic problem, Local coarsening of simplicial finite element meshes generated by bisections, Error reduction, convergence and optimality of an adaptive mixed finite element method, Optimal convergence behavior of adaptive FEM driven by simple \((h-h/2)\)-type error estimators, Optimal additive Schwarz methods for the \(hp\)-BEM: the hypersingular integral operator in 3D on locally refined meshes, Convergence of a standard adaptive nonconforming finite element method with optimal complexity, Quasi-optimal convergence rates for adaptive boundary element methods with data approximation. I: Weakly-singular integral equation, Functional a posteriori error estimates for boundary element methods, Adaptive finite element method for nonmonotone quasi-linear elliptic problems, Convergence of adaptive weak Galerkin finite element methods for second order elliptic problems, Uniform convergence of multigrid methods for adaptive meshes, Numerical results for adaptive (negative norm) constrained first order system least squares formulations, Collective marking for arbitrary order adaptive least-squares finite element methods with optimal rates, A coarsening algorithm on adaptive red-green-blue refined meshes, First-order least-squares method for the obstacle problem, Exponential convergence in \(H^1\) of \textit{hp}-FEM for Gevrey regularity with isotropic singularities, Strict bounding of quantities of interest in computations based on domain decomposition, Recurrent neural networks as optimal mesh refinement strategies, Convergence of adaptive stochastic collocation with finite elements, Robust localization of the best error with finite elements in the reaction-diffusion norm, The saturation assumption yields optimal convergence of two-level adaptive BEM, Longest-edge \(n\)-section algorithms: properties and open problems, Optimal convergence rates for goal-oriented FEM with quadratic goal functional, Uniform preconditioners of linear complexity for problems of negative order, Adaptive FEM with coarse initial mesh guarantees optimal convergence rates for compactly perturbed elliptic problems, Optimal quasi-diagonal preconditioners for pseudodifferential operators of order minus two, Quasi-optimality of adaptive mixed FEMs for non-selfadjoint indefinite second-order linear elliptic problems, Adaptive space-time finite element methods for parabolic optimal control problems, Energy norm based error estimators for adaptive BEM for hypersingular integral equations, An optimal adaptive FEM for eigenvalue clusters
Uses Software
Cites Work
- An algorithm for adaptive mesh refinement in \(n\) dimensions
- Design of adaptive finite element software. The finite element toolbox ALBERTA. With CD-ROM
- Adaptive finite element methods with convergence rates
- A recursive approach to local mesh refinement in two and three dimensions
- Simplicial grid refinement: On Freudenthal's algorithm and the optimal number of congruence classes
- Optimality of a standard adaptive finite element method
- Local mesh refinement in 2 and 3 dimensions
- Local Bisection Refinement for N-Simplicial Grids Generated by Reflection
- Data Oscillation and Convergence of Adaptive FEM
- Locally Adapted Tetrahedral Meshes Using Bisection
