Mon, 15.05.2023 13:30
Stability of LU-Factorizations and Optimality of Adaptive Algorithms
Abstract: We show that the optimality of a large class of adaptive finite element mesh refinement algorithms can be reduced to a stability bound on the factors of the standard LU-factorization of matrices. This new bound can be proved by use of Schatten norms and may be of independent interest for linear algebra.
For adaptive mesh refinement, it settles long standing open questions about the optimality of adaptive algorithms for indefinite and nonsymmetric problems such as the Stokes problem or time dependent equations.