Displaying similar documents to “Uniform convergence of local multigrid methods for the time-harmonic Maxwell equation∗”

Uniform convergence of local multigrid methods for the time-harmonic Maxwell equation

Huangxin Chen, Ronald H. W. Hoppe, Xuejun Xu (2013)

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique

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For the efficient numerical solution of indefinite linear systems arising from curl conforming edge element approximations of the time-harmonic Maxwell equation, we consider local multigrid methods (LMM) on adaptively refined meshes. The edge element discretization is done by the lowest order edge elements of Nédélec’s first family. The LMM features local hybrid Hiptmair smoothers of Jacobi and Gauss–Seidel type which are performed only on basis functions associated with newly created...

Discontinuous Galerkin methods for problems with Dirac delta source

Paul Houston, Thomas Pascal Wihler (2012)

ESAIM: Mathematical Modelling and Numerical Analysis

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In this article we study discontinuous Galerkin finite element discretizations of linear second-order elliptic partial differential equations with Dirac delta right-hand side. In particular, assuming that the underlying computational mesh is quasi-uniform, we derive an bound on the error measured in terms of the -norm. Additionally, we develop residual-based error estimators that can be used within an adaptive mesh refinement ...

Discontinuous Galerkin methods for problems with Dirac delta source

Paul Houston, Thomas Pascal Wihler (2012)

ESAIM: Mathematical Modelling and Numerical Analysis

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In this article we study discontinuous Galerkin finite element discretizations of linear second-order elliptic partial differential equations with Dirac delta right-hand side. In particular, assuming that the underlying computational mesh is quasi-uniform, we derive an bound on the error measured in terms of the -norm. Additionally, we develop residual-based error estimators that can be used within an adaptive mesh refinement ...

Convergence of some adaptive FEM-BEM coupling for elliptic but possibly nonlinear interface problems

Markus Aurada, Michael Feischl, Dirk Praetorius (2012)

ESAIM: Mathematical Modelling and Numerical Analysis

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We consider the symmetric FEM-BEM coupling for the numerical solution of a (nonlinear) interface problem for the 2D Laplacian. We introduce some new error estimators based on the ( − /2)-error estimation strategy. In particular, these include the approximation error for the boundary data, which allows to work with discrete boundary integral operators only. Using the concept of estimator reduction, we prove that the proposed adaptive algorithm is ...

Convergence of some adaptive FEM-BEM coupling for elliptic but possibly nonlinear interface problems

Markus Aurada, Michael Feischl, Dirk Praetorius (2012)

ESAIM: Mathematical Modelling and Numerical Analysis

Similarity:

We consider the symmetric FEM-BEM coupling for the numerical solution of a (nonlinear) interface problem for the 2D Laplacian. We introduce some new error estimators based on the ( − /2)-error estimation strategy. In particular, these include the approximation error for the boundary data, which allows to work with discrete boundary integral operators only. Using the concept of estimator reduction, we prove that the proposed adaptive algorithm is ...