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$$p$$-multigrid method for Fekete-Gauss spectral element approximations of elliptic problems. (English) Zbl 1364.65264
Summary: An efficient p-multigrid method is developed to solve the algebraic systems which result from the approximation of elliptic problems with the so-called Fekete-Gauss Spectral Element Method, which makes use of the Fekete points of the triangle as interpolation points and of the Gauss points as quadrature points. A multigrid strategy is defined by comparison of different prolongation/restriction operators and coarse grid algebraic systems. The efficiency and robustness of the approach, with respect to the type of boundary condition and to the structured/unstructured nature of the mesh, are highlighted through numerical examples.

##### MSC:
 65N35 Spectral, collocation and related methods for boundary value problems involving PDEs 65N55 Multigrid methods; domain decomposition for boundary value problems involving PDEs
##### Keywords:
spectral elements; Fekete points; multigrid methods
##### Software:
2Dhp90; Wesseling
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