A scalable and robust vertex-star relaxation for high-order FEM

• Published in: arXiv.org
• Main Authors: Brubeck, Pablo D, Farrell, Patrick E
• Format: Paper
• Language: English
• Published: Ithaca Cornell University Library, arXiv.org 11.10.2021
• Subjects: Cholesky factorization; Coercivity; Degrees of freedom; Finite difference method; Mathematical analysis; Polynomials; Robustness; Solvers; Stiffness matrix; Tensors

Pavarino proved that the additive Schwarz method with vertex patches and a low-order coarse space gives a \(p\)-robust solver for symmetric and coercive problems. However, for very high polynomial degree it is not feasible to assemble or factorize the matrices for each patch. In this work we introdu...