Session B6 - Multiresolution and Adaptivity in Numerical PDEs
July 15, 18:00 ~ 18:25 - Room T1
Rate optimal adaptivity for non-symmetric FEM/BEM coupling
UNSW Sydney, Australia - email@example.com
We develop a framework which allows us to prove the essential general quasi-orthogonality for the non-symmetric Johnson-Nédélec finite element/boundary element coupling. General quasi-orthogonality was first proposed in [Carstensen, Feischl, Page, Praetorius 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-Nédélec coupling converges with optimal rates. The developed techniques are fairly general and can most likely be applied to other problems like Stokes equation.