Search
Results
-
Fourier mode analysis of layers in shallow shell deformations
(1999)SAM Research ReportWe investigate here the length scales of the boundary or interior layer effects in shell deformation. Quantitative information on the layers is obtained by considering two (simplified) `shallow' shell models corresponding to the `classical' three-field (Love-Koiter-Novozhilov), resp. five-field (Reissner-Naghdi) shell models. We start by analysing the layers as functions of the thickness of the shell, while keeping the other geometric ...Report -
Homogenization via p-FEM for Problems with Microstructure
(1999)SAM Research ReportA new class of $p$ version FEM for elliptic problems with microstructure is developed. Based on arguments from the theory of $n$-widths, the existence of subspaces with favourable approximation properties for solution sets of PDEs is deduced. The construction of such subspaces is addressed for problems with (patch-wise) periodic microstructure. Families of adapted spectral shape functions are exhibited which give exponential convergence ...Report -
Generalized p-FEM in Homogenization
(1999)SAM Research ReportA new finite element method for elliptic problems with locally periodic microstructure of length $\varepsilon >0$ is developed and analyzed. It is shown that the method converges, as $\varepsilon \rightarrow 0$, to the solution of the homogenized problem with optimal order in $\varepsilon$ and exponentially in the number of degrees of freedom independent of $\varepsilon > 0$. The computational work of the method is bounded independently ...Report