Optimal Convergence Rates for Adaptive Lowest-Order Discontinuous Petrov--Galerkin Schemes

DOI10.1137/17M1146671zbMath1395.65140OpenAlexW2802064869MaRDI QIDQ4641591

Carsten Carstensen, Friederike Hellwig

Publication date: 18 May 2018

Published in: SIAM Journal on Numerical Analysis (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1137/17m1146671

zbMATH Keywords

adaptive mesh refinementerror estimatediscontinuous Petrov-Galerkin methodaxioms of adaptivityoptimal convergence rate.

Mathematics Subject Classification ID

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)

Related Items (5)

Adaptive Least-Squares, Discontinuous Petrov-Galerkin, and Hybrid High-Order Methods ⋮ A posteriori analysis for a mixed FEM discretization of the linear elasticity spectral problem ⋮ Adaptive guaranteed lower eigenvalue bounds with optimal convergence rates ⋮ Collective marking for adaptive least-squares finite element methods with optimal rates ⋮ Analysis of FEAST spectral approximations using the DPG discretization

Cites Work

• Unnamed Item
• Axioms of adaptivity
• Breaking spaces and forms for the DPG method and applications including Maxwell equations
• Mathematical aspects of discontinuous Galerkin methods.
• Nonlinear discontinuous Petrov-Galerkin methods
• Adaptive finite element methods with convergence rates
• Constants in discrete Poincaré and Friedrichs inequalities and discrete quasi-interpolation
• Convergence of natural adaptive least squares finite element methods
• Guaranteed lower eigenvalue bounds for the biharmonic equation
• Optimality of a standard adaptive finite element method
• Low-order dPG-FEM for an elliptic PDE
• Convergence rates of the DPG method with reduced test space degree
• Adaptivity and variational stabilization for convection-diffusion equations
• A Review of Unified A Posteriori Finite Element Error Control
• Discrete Reliability for Crouzeix--Raviart FEMs
• Convergence and Optimality of Adaptive Least Squares Finite Element Methods
• A class of discontinuous Petrov-Galerkin methods. II. Optimal test functions
• Analysis of the DPG Method for the Poisson Equation
• A new error analysis for discontinuous finite element methods for linear elliptic problems
• Theory of adaptive finite element methods: An introduction
• Quasi-Optimal Convergence Rate for an Adaptive Finite Element Method
• An Inexpensive Method for the Evaluation of the Solution of the Lowest Order Raviart–Thomas Mixed Method
• Axioms of Adaptivity with Separate Marking for Data Resolution
• An Adaptive Least-Squares FEM for Linear Elasticity with Optimal Convergence Rates
• Comparison Results of Finite Element Methods for the Poisson Model Problem
• Mixed Finite Element Methods and Applications
• Adaptive nonconforming Crouzeix-Raviart FEM for eigenvalue problems
• A Posteriori Error Control for DPG Methods
• The completion of locally refined simplicial partitions created by bisection
• The Mathematical Theory of Finite Element Methods
• Low-Order Discontinuous Petrov--Galerkin Finite Element Methods for Linear Elasticity
• Finite Elements

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