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Orthogonal hp-FEM for Elliptic Problems Based on a Non-Affine Concept

In: Numerical Mathematics and Advanced Applications

Author

Listed:
  • Pavel Šolín

    (University of Texas at El Paso, Department of Mathematical Sciences)

  • Tomáš Vejchodský

    (Academy of Sciences, Mathematical Institute)

  • Martin Zítka

    (University of Texas at El Paso, Department of Mathematical Sciences)

Abstract

In this paper we propose and test a new non-affine concept of hierarchic higher-order finite elements (hp-FEM) suitable for symmetric linear elliptic problems. The energetic inner product induced by the elliptic operator is used to construct partially orthonormal shape functions which automatically eliminate all internal degrees of freedom from the stiffness matrix. The stiffness matrix becomes smaller and better-conditioned compared to standard types of higher-order shape functions. The orthonormalization algorithm is elementwise local and therefore easily parallelizable. The procedure is extendable to nonsymmetric elliptic problems. Numerical examples including performance comparisons to other popular sets of higher-order shape functions are presented.

Suggested Citation

  • Pavel Šolín & Tomáš Vejchodský & Martin Zítka, 2006. "Orthogonal hp-FEM for Elliptic Problems Based on a Non-Affine Concept," Springer Books, in: Alfredo Bermúdez de Castro & Dolores Gómez & Peregrina Quintela & Pilar Salgado (ed.), Numerical Mathematics and Advanced Applications, pages 683-690, Springer.
    • Handle: RePEc:spr:sprchp:978-3-540-34288-5_66
    DOI: 10.1007/978-3-540-34288-5_66
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