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On polynomial reproduction of dual FE bases. (English) Zbl 1026.65098
Debit, N. (ed.) et al., Domain decomposition methods in science and engineering. Papers of the thirteenth international conference on domain decomposition methods, Lyon, France, October 9-12, 2000. Barcelona: International Center for Numerical Methods in Engineering (CIMNE). Theory Eng. Appl. Comput. Methods. 85-96 (2002).
From the introduction: We construct local piecewise polynomial dual bases for standard Lagrange finite element (FE) spaces which themselves provide maximal polynomial reproduction. By means of such dual bases for the Lagrange multiplier, extremely efficient realization of mortar methods on nonmatching triangulations can be obtained without losing the optimality of the discretization errors. In contrast to the standard mortar approach, the locality of the constrained basis functions is preserved. The construction of dual bases and quasi-interpolants for univariate spline spaces is well-understood. However, the dual space is usually of a more complicated structure, and cannot be fixed beforehand.
For the entire collection see [Zbl 1011.00036].

65N30 Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs
65N55 Multigrid methods; domain decomposition for boundary value problems involving PDEs
65T60 Numerical methods for wavelets
35J25 Boundary value problems for second-order elliptic equations