Higher-order numerical methods for transient wave equations / Gary C. Cohen. p. cm. --(Scientific computation, ISSN 1434-8322) Inc1udes bibliographical references and index.

Solving the wave equation by a C o finite element method requires to mass-lump the term in time of the variational f6rmulation in order to avoid the inversion of a n-diagonal symmetric matrix at each time-step of the algorithm. One can easily get this mass-lumping on quadrilateral meshes by using a h-version of the spectral elements, based on Gauss-Lobatto quadrature formulae but the equivalent method is not obvious for triangular meshes. In this paper we construct and analyze new families of triangular finite elements which fulfill the same requirements as spectral quadratic and cubic finite elements.

Higher-order numerical methods for transient wave equations / Gary C. Cohen. p. cm. --(Scientific computation, ISSN 1434-8322) Inc1udes bibliographical references and index.

We provide a comprehensive study of arbitrarily high-order finite elements defined on pyramids. We propose a new family of high-order nodal pyramidal finite element which can be used in hybrid meshes which include hexahedra, tetrahedra, wedges and pyramids. Finite elements matrices can be evaluated through approximate integration, and we show that the order of convergence of the method is conserved. Numerical results demonstrate the efficiency of hybrid meshes compared to pure tetrahedral meshes or hexahedral meshes obtained by splitting tetrahedra into hexahedra.

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