Uniform Schwarz Preconditioners
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Related Articles from SNS
Uniform Schwarz Preconditioners for Variable-Degree $hp$ Finite Element Interface Problems
arXiv:2606.03141v1 Announce Type: new Abstract: We construct $h$- and $p$-robust, degree-preserving space decompositions and additive Schwarz preconditioners for variable-degree $hp$ finite element discretizations of reaction-diffusion and fitted-interface problems. On conforming simplicial meshes in arbitrary dimension, the single-domain result allows an arbitrary elementwise degree distribution subject only to $p_K\ge1$. A minimal-average Falk--Winther bubble transform is introduced by...
Stable Triangle Projections for Variable-Degree Tetrahedral Spaces and Uniform IPDG Preconditioning
Announce Type: new Abstract: The main ingredient of this paper is an edge-local variable-degree projection on a triangle that is uniformly stable in both L2 and H1. We use this two-dimensional operator in two tetrahedral constructions. First, on a reference tetrahedron, we build an H1-stable projection from a high order polynomial space onto a variable-degree space whose degrees are prescribed independently on edges, faces, and in the volume.