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High order finite elements for material and geometric nonlinear finite strain problemsHeisserer, Ulrich January 2008 (has links)
Zugl.: München, Techn. Univ., Diss., 2008
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Finite-Elemente-Methoden zur räumlichen Diskretisierung von Mehrfeldproblemen der Strukturmechanik unter Berücksichtigung diskreter RisseBecker, Christian January 2007 (has links)
Zugl.: Bochum, Univ., Diss., 2007
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p-FEM quadrature error analysis on tetrahedraEibner, Tino, Melenk, Jens Markus 30 November 2007 (has links) (PDF)
In this paper we consider the p-FEM for elliptic boundary value problems on tetrahedral meshes where the entries of the stiffness matrix are evaluated by numerical quadrature. Such a quadrature can be done by mapping the tetrahedron to a hexahedron via the Duffy transformation.
We show that for tensor product Gauss-Lobatto-Jacobi quadrature formulas with q+1=p+1 points in each direction and shape functions that are adapted to the quadrature formula, one again has discrete stability for the fully discrete p-FEM.
The present error analysis complements the work [Eibner/Melenk 2005] for the p-FEM on triangles/tetrahedra where it is shown that by adapting the shape functions to the quadrature formula, the stiffness matrix can be set up in optimal complexity.
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p-FEM quadrature error analysis on tetrahedraEibner, Tino, Melenk, Jens Markus 30 November 2007 (has links)
In this paper we consider the p-FEM for elliptic boundary value problems on tetrahedral meshes where the entries of the stiffness matrix are evaluated by numerical quadrature. Such a quadrature can be done by mapping the tetrahedron to a hexahedron via the Duffy transformation.
We show that for tensor product Gauss-Lobatto-Jacobi quadrature formulas with q+1=p+1 points in each direction and shape functions that are adapted to the quadrature formula, one again has discrete stability for the fully discrete p-FEM.
The present error analysis complements the work [Eibner/Melenk 2005] for the p-FEM on triangles/tetrahedra where it is shown that by adapting the shape functions to the quadrature formula, the stiffness matrix can be set up in optimal complexity.
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