On the mortar element method: Generalizations and implementation. (English) Zbl 0704.65077

Anagnostou, George; Maday, Yvon; Mavriplis, Catherine; Patera, Anthony T.

Domain decomposition methods for partial differential equations, Proc. 3rd Int. Symp. Houston/TX (USA) 1989, 157-173 (1990).

[For the entire collection see Zbl 0695.00026.]
The mortar element method is a nonconforming discretization based on the explicit construction of an optimal approximation space; in particular, it leads to efficient implementation on parallel supercomputers. This paper presents several enhancements to the spectral element version of the mortar method: i) arbitrary two-dimensional element topologies; ii) the application to moving-geometry sliding-mesh problems; iii) the development of new data structures based on composite data objects and topology trees which allow for simple implementation of complex discretizations.

Reviewer: M.Bernadou

MSC:

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
65N35	Spectral, collocation and related methods for boundary value problems involving PDEs
65Y05	Parallel numerical computation
65N50	Mesh generation, refinement, and adaptive methods for boundary value problems involving PDEs
35J25	Boundary value problems for second-order elliptic equations

Keywords:

decomposition method; mortar element method; parallel supercomputers; spectral element; two-dimensional element topologies; moving-geometry sliding-mesh problems; composite data objects; topology trees; complex discretizations