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Hierarchic Models for Laminated Plates and Shells
(1997)SAM Research ReportThe definition, essential properties and formulation of hierarchic models for laminated plates and shells are presented. The hierarchic models satisfy three essential requirements: approximability; asymptotic consistency, and optimality of convergence rate. Aspects of implementation are discussed and the performance characteristics are illustrated by examples.Report -
Fast numerical solution of the linearized Molodensky problem
(1999)SAM Research ReportWhen standard boundary element methods (BEM) are used to solve the linearized vector Molodensky problem we are confronted with two problems: (i) the absence of $O(|x|^{-2})$ terms in the decay condition is not taken into account, since the single layer ansatz, which is commonly used as representation of the perturbation potential, is of the order $O(|x|^{-1})$ as $x \to \infty$. This implies that the standard theory of Galerkin BEM is not ...Report -
HP90: a general & flexible fortran 90 hp-FE code
(1997)SAM Research ReportA general 2D-$hp$-adaptive Finite Element (FE) implementation inFortran 90 is described. The implementation is based on an abstractdata structure, which allows to incorporate the full $hp$-adaptivityof triangular and quadrilateral finite elements.The $h$-refinement strategies are based on $h2$-refinement ofquadrilaterals and $h4$-refinement of triangles. For $p$-refinementwe allow the approximation order to vary within any element. The ...Report -
On coupled problems for viscous flow in exterior domains
(1996)SAM Research ReportThe use of the complete Navier-Stokes system in an unbounded domain is not always convenient in computations and, therefore, the Navier-Stokes problem is often truncated to a bounded domain. In this paper we simulate the interaction between the flow in this domain and the exterior flow with the aid of a coupled problem. We propose in particular a linear approximation of the exterior flow (here the Stokes flow or potential flow) coupled ...Report -
The hp-Version of the Streamline Diffusion Finite Element Method in Two Space Dimensions
(1999)SAM Research ReportThe Streamline Diffusion Finite Element Method (SDFEM) for a two dimensional convection-diffusion problem is analyzed in the context of the hp-version of the Finite Element Method (FEM). It is proved that the appropriate choice of the SDFEM parameters leads to stable methods on the class of "boundary layer meshes" which may contain anisotropic needle elements of arbitrarily high aspect ratio. Consistency results show that the use of such ...Report -
hp-FEM for Hyperbolic Problems
(1999)SAM Research ReportThis paper is devoted to the a priori and a posteriori error analysis of the hp-version of the discontinuous Galerkin finite element method for partial differential equations of hyperbolic and nearly-hyperbolic character. We consider second-order partial differential equations with nonnegative characteristic form, a large class of equations which includes convection-dominated diffusion problems, degenerate elliptic equations and second-order ...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 -
Advanced boundary element algorithms
(1999)SAM Research ReportWe review recent algorithmic developments in the boundary element method (BEM) for large scale engineering calculations. Two classes of algorithms, the clustering and the wavelet-based schemes are compared. Both have $O(N(\log N)^a)$ complexity with some small $a \ge 0$ and allow in-core simulations with up to $N = O(10^6)$ DOF on the boundary on serial workstations. Clustering appears more robust for complex surfaces.Report -
A spectral Garlekin method for hydrodynamic stability problems
(1998)SAM Research ReportA spectral Galerkin method for calculating the eigenvalues of the Orr-Sommerfeld equation is presented. The matrices of the resulting generalized eigenvalue problem are sparse. A convergence analysis of the method is presented which indicates that a) no spurious eigenvalues occur and b) reliable results can only be expected under the assumption of {\em scale resolution}, i.e., that $\re/p^2$ is small; here $\re$ is the Reynolds number and ...Report -
Mixed hp Finite Element Methods for Stokes and Non-Newtonian Flow
(1997)SAM Research ReportWe analyze the stability of hp finite elements for viscous incompressible flow. For the classical velocity-pressure formulation, we give new estimates for the discrete inf-sup constants on geometric meshes which are explicit in the polynomial degree k of the elements. In particular, we obtain new bounds for p-elements on triangles. For the three-field Stokes problem describing linearized non-Newtonian flow, we estimate discrete inf-sup ...Report