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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 -
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 -
hp-FEM for incompressible fluid flow - stable and stabilized
(1997)SAM Research ReportThe stable Galerkin formulation and a stabilized Galerkin Least Squares formulation for the Stokes problem are analyzed in the context of the hpversion of the Finite Element Method (FEM). Theoretical results for both formulations establish exponential rates of convergence and are confirmed by intensive numerical convergence studies. In our numerical experiments we demonstrate that these hp-FEM with geometric mesh refinement can resolve ...Report -
Synchronization issues in distributed applications: definitions, problems, and quality of synchronization
(1997)TIK ReportIn this report synchronization issues arising in distributed applications are discussed. A general and detailed introduction to the field of synchronization is provided. General terms related to synchronization as well as concepts are introduced, defined and discussed in short. The specific problem fields of synchronization in multi-party environments and in presence of control commands are introduced. A discussion of some of the numerous ...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 -
Wavelet Galerkin Algorithms for Boundary Integral Equations
(1997)SAM Research ReportThe implementation of a fast, wavelet-based Galerkin discretization of second kind integral equations on piecewise smooth surfaces $\Gamma\subset \R^3$ is described. It allows meshes consisting of triangles as well as quadrilaterals. The algorithm generates a sparse, approximate stiffness matrix with $N=O(N(log N)^2)$ nonvanishing entries in $O(N(\log N)^4)$ operations where N is the number of degrees of freedom on the boundary while ...Report -
The Method of Transport for mixed hyperbolic-parabolic systems
(1997)SAM Research ReportStarting from a numerical scheme for solving systems of hyperbolic partial differential equations the transition to parabolic equations of the type of advection-diffusion equations needs a different treatment of the viscous part. Since we are using a genuine multi-dimensional scheme also the fact that the diffusion acts in infinitely many directions shall be captured properly. Therefore, to be able to use this scheme we have developed a ...Report -
Error Estimators for the Position of Discontinuities in Hyperbolic Conservation Laws with Source Terms which are solved using Operator Splitting
(1997)SAM Research ReportWhen computing numerical solutions of hyperbolic conservation laws with source terms, one may obtain spurious solutions --- these are unphysical solutions that only occur in numerics such as shock waves moving with wrong speeds, cf. [7], [2], [1], [10], [3]. Therefore it is important to know how errors of the location of a discontinuity can be controlled. To derive appropriate error-estimates and to use them to control such errors, is the ...Report