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
...
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
...
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...
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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