Year: 2017
Type: preprint
Abstract: We develop a framework which allows us to prove the essential general quasi-orthogonality for the non-symmetric Johnson-Nedelec finite element/boundary element coupling. General quasi-orthogonality was first proposed in [Axioms of Adaptivity, 2014] as a necessary ingredient of optimality proofs and is the major difficulty on the way to prove rate optimal convergence of adaptive algorithms for many strongly non-symmetric problems. The proof exploits a new connection between the general quasi-orthogonality and LU-factorization of infinite matrices. We then derive that a standard adaptive algorithm for the Johnson-Nedelec coupling converges with optimal rates. The developed techniques are fairly general and can most likely be applied to other problems like Stokes equation.
Source: arXiv (Cornell University)
Author: Feischl, Michael
Language: English
Subfield: Computational Mechanics
Field: Engineering
Domain: Physical Sciences
Open Access status: green
Funder: Austrian Science Fund
OpenAlex ID: W2765456836