{
  "id": "1710.06082",
  "version": "v1",
  "published": "2017-10-17T04:13:19.000Z",
  "updated": "2017-10-17T04:13:19.000Z",
  "title": "Optimal adaptivity for non-symmetric FEM/BEM coupling",
  "authors": [
    "Michael Feischl"
  ],
  "categories": [
    "math.NA"
  ],
  "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.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2017-10-17T04:13:19.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "non-symmetric fem/bem coupling",
      "optimal adaptivity",
      "finite element/boundary element coupling",
      "general quasi-orthogonality",
      "non-symmetric johnson-nedelec finite element/boundary element"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}