Schwarz Methods with Local Refinement for the p-Version Finite Element Method
Pavarino, Luca F.
We study local refinement for an additive Schwarz method with overlap using the p-version finite element method, introduced in a previous paper. We consider linear, scalar, self-adjoint, second order elliptic problems and quadrilateral finite elements in the discretization. We prove an optimal bound for the condition number of the iteration operator under certain hypotheses on the refinement region, in two and three dimensions. In the general two dimensional case, we obtain an almost optimal bound with logarithmic growth in p. Like other Schwarz methods, these algorithms are highly parallel.
Citable link to this pagehttps://hdl.handle.net/1911/101784
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