Biorthogonal bases with local support and approximation properties

Lamichhane, Bishnu; Wohlmuth, Barbara

doi:10.1090/S0025-5718-06-01907-7

Biorthogonal bases with local support and approximation properties
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by Bishnu P. Lamichhane and Barbara I. Wohlmuth PDF

Math. Comp. 76 (2007), 233-249 Request permission

Abstract:

We construct locally supported basis functions which are biorthogonal to conforming nodal finite element basis functions of degree $p$ in one dimension. In contrast to earlier approaches, these basis functions have the same support as the nodal finite element basis functions and reproduce the conforming finite element space of degree $p-1$. Working with Gauß–Lobatto nodes, we find an interesting connection between biorthogonality and quadrature formulas. One important application of these newly constructed biorthogonal basis functions are two-dimensional mortar finite elements. The weak continuity condition of the constrained mortar space is realized in terms of our new dual bases. As a result, local static condensation can be applied which is very attractive from the numerical point of view. Numerical results are presented for cubic mortar finite elements.

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