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Mixed hp-FEM on anisotropic meshes
(1997)SAM Research ReportMixed hp-FEM for incompressible fluid flow on anisotropic meshes are analyzed. A discrete inf-sup condition is proved with a constant independent of the meshwidth and the aspect ratio. For each polynomial degree $k\geq 2$, velocity-pressure subspace pairs are presented which are stable on quadrilateral mesh-patches, independently of the element aspect ratio implying in particular divergence stability on the so-called Shishkin-meshes. ...Report -
Mixed hp-FEM on anisotropic meshes II: Hanging nodes and tensor products of boundary layer meshes
(1997)SAM Research ReportDivergence stability of mixed hp-FEM for incompressible fluid flow for a general class of possibly highly irregular meshes is shown. The meshes may be refined anisotropically and contain hanging nodes on geometric patches. The inf-sup constant is independent of the aspect ratio of the elements and the dependence on the polynomial degree is given explicitly. Numerical estimates of inf-sup constants confirm our results.Report -
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Two notes on the implementation of wavelet Galerkin boundary element methods
(1997)SAM Research ReportWe report, in two notes, recent progress in the implementation of wavelet-based Galerkin BEM on polyhedra and study the performance.Report -
An Accuracy Barrier for Stable Three-Time-Level DifferenceSchemes for Hyperbolic Equations
(1997)SAM Research ReportWe consider three-time-level difference schemes for the linear constant coefficient advection equation $u_t$ = $cu_x$. In 1985 it was conjectured that the varrier to the local order $p$ of schemes which are stable is giben by $p \le $2 min {$R$,$S$}. Here $R$ and $S$ denote the number of downwind and upwind points, respectively, in the difference stencil with respect to the characteristic of the differential equation through the update ...Report -
Regularity of interacting nonspherical Fermi surfaces: the exact self-energy
(1997)FIM's preprintsReport -
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 -
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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