A short note on plain convergence of adaptive least-squares finite element methods
From MaRDI portal
Publication:2210600
DOI10.1016/j.camwa.2020.07.022zbMath1451.65189arXiv2005.11015OpenAlexW3027085067MaRDI QIDQ2210600
Thomas Führer, Dirk Praetorius
Publication date: 7 November 2020
Published in: Computers \& Mathematics with Applications (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/2005.11015
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) Iterative numerical methods for linear systems (65F10) Mesh generation, refinement, and adaptive methods for boundary value problems involving PDEs (65N50) Preconditioners for iterative methods (65F08)
Related Items
Adaptive Least-Squares, Discontinuous Petrov-Galerkin, and Hybrid High-Order Methods ⋮ Plain convergence of goal-oriented adaptive FEM ⋮ How to prove optimal convergence rates for adaptive least-squares finite element methods ⋮ Collective marking for arbitrary order adaptive least-squares finite element methods with optimal rates ⋮ Further results on a space-time FOSLS formulation of parabolic PDEs
Cites Work
- Unnamed Item
- Axioms of adaptivity
- On 2D newest vertex bisection: optimality of mesh-closure and \(H ^{1}\)-stability of \(L _{2}\)-projection
- Adaptive BEM with inexact PCG solver yields almost optimal computational costs
- Least-squares finite element methods
- Feedback and adaptive finite element solution of one-dimensional boundary value problems
- Adaptive finite element methods with convergence rates
- A linear Uzawa-type FEM-BEM solver for nonlinear transmission problems
- Convergence of natural adaptive least squares finite element methods
- Optimality of a standard adaptive finite element method
- Stopping Criteria for Adaptive Finite Element Solvers
- Convergence and Optimality of Adaptive Least Squares Finite Element Methods
- A convergence proof for adaptive finite elements without lower bound
- An adaptive least squares mixed finite element method for the stress-displacement formulation of linear elasticity
- Finite elements in computational electromagnetism
- Finite Element Interpolation of Nonsmooth Functions Satisfying Boundary Conditions
- A BASIC CONVERGENCE RESULT FOR CONFORMING ADAPTIVE FINITE ELEMENTS
- Quasi-Optimal Convergence Rate for an Adaptive Finite Element Method
- Finite Element Methods for Navier-Stokes Equations
- First-Order System Least Squares for Second-Order Partial Differential Equations: Part I
- Data Oscillation and Convergence of Adaptive FEM
- Rate optimal adaptive FEM with inexact solver for nonlinear operators
- Asymptotic Exactness of the Least-Squares Finite Element Residual
- An Adaptive Least-Squares FEM for Linear Elasticity with Optimal Convergence Rates
- Least-Squares Methods for Incompressible Newtonian Fluid Flow: Linear Stationary Problems
- Finite Element Methods for Maxwell's Equations
- A Convergent Adaptive Algorithm for Poisson’s Equation
- Mixed Finite Element Methods and Applications
- Dörfler marking with minimal cardinality is a linear complexity problem
- Collective marking for adaptive least-squares finite element methods with optimal rates
- Variational Formulation and Numerical Analysis of Linear Elliptic Equations in Nondivergence form with Cordes Coefficients
- Convergence and optimality of adaptive edge finite element methods for time-harmonic Maxwell equations
- The completion of locally refined simplicial partitions created by bisection
- The Mathematical Theory of Finite Element Methods
