Global ETD Search

1	A local error analysis of the boundary concentrated FEM Eibner, 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. local error ddc:510 Elliptisches Randwertproblem Interpolationsoperator hp-Methode
2	A local error analysis of the boundary concentrated FEM Eibner, 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. info:eu-repo/classification/ddc/510 ddc:510 Elliptisches Randwertproblem Interpolationsoperator hp-Methode local error
3	A posteriori error estimation for non-linear eigenvalue problems for differential operators of second order with focus on 3D vertex singularities Pester, 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. Clement-type interpolation a posteriori error estimation corner singularities non-linear eigenvalue problems spectral theory two-dimensional manifolds unit sphere ddc:510 Eigenwertproblem Fehlerabschätzung Interpolation Interpolationsoperator Singularität <Mathematik>
4	A posteriori error estimation for non-linear eigenvalue problems for differential operators of second order with focus on 3D vertex singularities Pester, 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. info:eu-repo/classification/ddc/510 ddc:510 Eigenwertproblem Fehlerabschätzung Interpolation Interpolationsoperator Singularität <Mathematik> Clement-type interpolation a posteriori error estimation corner singularities non-linear eigenvalue problems spectral theory two-dimensional manifolds unit sphere

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