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Discontinuous Galerkin methods for problems with Dirac delta source

Paul HoustonThomas Pascal Wihler — 2012

ESAIM: Mathematical Modelling and Numerical Analysis

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 HoustonThomas Pascal Wihler — 2012

ESAIM: Mathematical Modelling and Numerical Analysis

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 ...

Mixed discontinuous Galerkin approximation of the Maxwell operator : the indefinite case

Paul HoustonIlaria PerugiaAnna SchneebeliDominik Schötzau — 2005

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

We present and analyze an interior penalty method for the numerical discretization of the indefinite time-harmonic Maxwell equations in mixed form. The method is based on the mixed discretization of the curl-curl operator developed in [Houston et al., J. Sci. Comp. 22 (2005) 325–356] and can be understood as a non-stabilized variant of the approach proposed in [Perugia et al., Comput. Methods Appl. Mech. Engrg. 191 (2002) 4675–4697]. We show the well-posedness of this approach and derive optimal...

Mixed discontinuous Galerkin approximation of the Maxwell operator: The indefinite case

Paul HoustonIlaria PerugiaAnna SchneebeliDominik Schötzau — 2010

ESAIM: Mathematical Modelling and Numerical Analysis

We present and analyze an interior penalty method for the numerical discretization of the indefinite time-harmonic Maxwell equations in mixed form. The method is based on the mixed discretization of the curl-curl operator developed in [Houston , (2005) 325–356] and can be understood as a non-stabilized variant of the approach proposed in [Perugia , (2002) 4675–4697]. We show the well-posedness of this approach and derive optimal error estimates in the energy-norm as...

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