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A local error analysis of the boundary concentrated FEMEibner, Tino, Melenk, Jens Markus 01 September 2006 (has links) (PDF)
The boundary concentrated finite element method is
a variant of the hp-version of the FEM that is
particularly suited for the numerical treatment of
elliptic boundary value problems with smooth
coefficients and boundary conditions with low
regularity or non-smooth geometries. In this paper
we consider the case of the discretization of a
Dirichlet problem with exact solution
$u \in H^{1+\delta}(\Omega)$ and investigate the
local error in various norms. We show that for
a $\beta > 0$ these norms behave as
$O(N^{−\delta−\beta})$, where $N$ denotes the
dimension of the underlying finite element space.
Furthermore, we present a new Gauss-Lobatto based
interpolation operator that is adapted to the
case non-uniform polynomial degree distributions.
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A local error analysis of the boundary concentrated FEMEibner, Tino, Melenk, Jens Markus 01 September 2006 (has links)
The boundary concentrated finite element method is
a variant of the hp-version of the FEM that is
particularly suited for the numerical treatment of
elliptic boundary value problems with smooth
coefficients and boundary conditions with low
regularity or non-smooth geometries. In this paper
we consider the case of the discretization of a
Dirichlet problem with exact solution
$u \in H^{1+\delta}(\Omega)$ and investigate the
local error in various norms. We show that for
a $\beta > 0$ these norms behave as
$O(N^{−\delta−\beta})$, where $N$ denotes the
dimension of the underlying finite element space.
Furthermore, we present a new Gauss-Lobatto based
interpolation operator that is adapted to the
case non-uniform polynomial degree distributions.
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A posteriori error estimation for non-linear eigenvalue problems for differential operators of second order with focus on 3D vertex singularitiesPester, Cornelia 07 May 2006 (has links) (PDF)
This thesis is concerned with the finite element
analysis and the a posteriori error estimation for
eigenvalue problems for general operator pencils on
two-dimensional manifolds.
A specific application of the presented theory is the
computation of corner singularities.
Engineers use the knowledge of the so-called singularity
exponents to predict the onset and the propagation of
cracks.
All results of this thesis are explained for two model
problems, the Laplace and the linear elasticity problem,
and verified by numerous numerical results.
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A posteriori error estimation for non-linear eigenvalue problems for differential operators of second order with focus on 3D vertex singularitiesPester, Cornelia 21 April 2006 (has links)
This thesis is concerned with the finite element
analysis and the a posteriori error estimation for
eigenvalue problems for general operator pencils on
two-dimensional manifolds.
A specific application of the presented theory is the
computation of corner singularities.
Engineers use the knowledge of the so-called singularity
exponents to predict the onset and the propagation of
cracks.
All results of this thesis are explained for two model
problems, the Laplace and the linear elasticity problem,
and verified by numerous numerical results.
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