$L^\infty$ Norm Error Estimates for HDG Methods Applied to the Poisson Equation with an Application to the Dirichlet Boundary Control Problem
DOI10.1137/20M1338551zbMath1472.65142arXiv2005.07805OpenAlexW3136613310MaRDI QIDQ5855639
Yangwen Zhang, Gang Chen, Peter B. Monk
Publication date: 19 March 2021
Published in: SIAM Journal on Numerical Analysis (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/2005.07805
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) Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation (35J05) Numerical methods for partial differential equations, boundary value problems (65N99)
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Cites Work
- Unnamed Item
- Max-norm estimates for Stokes and Navier-Stokes approximations in convex polyhedra
- Optimal \(L^{\infty}\)-error estimates for nonconforming and mixed finite element methods of lowest order
- Asymptotic expansions and \(L^{\infty}\)-error estimates for mixed finite element methods for second order elliptic problems
- On optimal \(L^2\)- and surface flux convergence in FEM
- Error estimates for Dirichlet control problems in polygonal domains: quasi-uniform meshes
- Maximum-norm stability of the finite element Stokes projection
- A superconvergent hybridizable discontinuous Galerkin method for Dirichlet boundary control of elliptic PDEs
- Error estimates for variational normal derivatives and Dirichlet control problems with energy regularization
- Superconvergent interpolatory HDG methods for reaction diffusion equations. I: An \(HDG_k\) method
- An analysis of the minimal dissipation local discontinuous Galerkin method for convection-diffusion problems
- Pointwise error estimates of finite element approximations to the Stokes problem on convex polyhedra
- Error Analysis for a Finite Element Approximation of Elliptic Dirichlet Boundary Control Problems
- Quasi-Optimal Approximation of Surface Based Lagrange Multipliers in Finite Element Methods
- Error analysis in $L^p \leqslant p \leqslant \infty $, for mixed finite element methods for linear and quasi-linear elliptic problems
- Sharp Maximum Norm Error Estimates for Finite Element Approximations of the Stokes Problem in 2 - D
- Unified Hybridization of Discontinuous Galerkin, Mixed, and Continuous Galerkin Methods for Second Order Elliptic Problems
- Local and pointwise error estimates of the local discontinuous Galerkin method applied to the Stokes problem
- A projection-based error analysis of HDG methods
- Sharp maximum norm error estimates for general mixed finite element approximations to second order elliptic equations
- On the Quasi-Optimality in $L_\infty$ of the $\overset{\circ}{H}^1$-Projection into Finite Element Spaces*
- Optimal L ∞ Estimates for the Finite Element Method on Irregular Meshes
- $L_\infty $-convergence of saddle-point approximations for second order problems
- Interior Maximum Norm Estimates for Finite Element Methods
- Regularity estimates for elliptic boundary value problems in Besov spaces
- A New HDG Method for Dirichlet Boundary Control of Convection Diffusion PDEs II: Low Regularity
- Pointwise error estimates of the local discontinuous Galerkin method for a second order elliptic problem
- Local error analysis of the interior penalty discontinuous Galerkin method for second order elliptic problems
- Interior Maximum-Norm Estimates for Finite Element Methods, Part II
- An HDG Method for Dirichlet Boundary Control of Convection Dominated Diffusion PDEs
- Finite Element Error Estimates for Normal Derivatives on Boundary Concentrated Meshes
- Quasi-optimal a priori estimates for fluxes in mixed finite element methods and an application to the Stokes-Darcy coupling
- Pointwise Error Estimates for Finite Element Solutions of the Stokes Problem