Abstract nonconforming error estimates and application to boundary penalty methods for diffusion equations and time-harmonic Maxwell's equations

DOI10.1515/cmam-2017-0058zbMath1401.65132OpenAlexW2738063727MaRDI QIDQ1989693

Alexandre Ern, Jean-Luc Guermond

Publication date: 26 October 2018

Published in: Computational Methods in Applied Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1515/cmam-2017-0058

zbMATH Keywords

error estimatesfinite elementselliptic equationsdiscontinuous GalerkinNitsche methodCrouzeix-Raviart methodnonconforming methodsminimum regularity

Mathematics Subject Classification ID

Diffusion (76R50) 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) Maxwell equations (35Q61)

Related Items

A third Strang lemma and an Aubin-Nitsche trick for schemes in fully discrete formulation ⋮ Local decay rates of best-approximation errors using vector-valued finite elements for fields with low regularity and integrable curl or divergence ⋮ Preface: An eclectic view on numerical methods for PDEs: presentation of the special issue ``Advanced numerical methods: recent developments, analysis and applications ⋮ Quasi-optimal nonconforming approximation of elliptic PDEs with contrasted coefficients and \(H^{1+r}, r>0\), regularity ⋮ Numerical Analysis for Maxwell Obstacle Problems in Electric Shielding

Cites Work

• Mathematical aspects of discontinuous Galerkin methods.
• Mollification in strongly Lipschitz domains with application to continuous and discrete de Rham complexes
• Functional analysis, Sobolev spaces and partial differential equations
• Theory and practice of finite elements.
• Regularity of the Maxwell equations in heterogeneous media and Lipschitz domains
• Approximation variationnelle des problèmes aux limites
• Geometric and transformational properties of Lipschitz domains, Semmes-Kenig-Toro domains, and other classes of finite perimeter domains
• Über ein Variationsprinzip zur Lösung von Dirichlet-Problemen bei Verwendung von Teilräumen, die keinen Randbedingungen unterworfen sind. (On a variational principle for solving Dirichlet problems less boundary conditions using subspaces)
• Error indicators for the mortar finite element discretization of the Laplace equation
• A new error analysis for discontinuous finite element methods for linear elliptic problems
• Medius analysis and comparison results for first-order finite element methods in linear elasticity
• Vector potentials in three-dimensional non-smooth domains
• BASIC PRINCIPLES OF VIRTUAL ELEMENT METHODS
• Finite Elemente
• Finite element quasi-interpolation and best approximation
• Error analysis of discontinuous Galerkin methods for the Stokes problem under minimal regularity
• A posteriori error estimates for Maxwell equations
• Discontinuous Galerkin Methods for Friedrichs' Systems. I. General theory
• The Identity of Weak and Strong Extensions of Differential Operators
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item