{
  "id": "1807.11802",
  "version": "v1",
  "published": "2018-07-31T13:19:05.000Z",
  "updated": "2018-07-31T13:19:05.000Z",
  "title": "Adaptive BEM with optimal convergence rates for the Helmholtz equation",
  "authors": [
    "Alex Bespalov",
    "Timo Betcke",
    "Alexander Haberl",
    "Dirk Praetorius"
  ],
  "categories": [
    "math.NA"
  ],
  "abstract": "We analyze an adaptive boundary element method for the weakly-singular and hypersingular integral equations for the 2D and 3D Helmholtz problem. The proposed adaptive algorithm is steered by a residual error estimator and does not rely on any {\\sl a priori} information that the underlying meshes are sufficiently fine. %Instead, adaptive mesh-refinement leads to We prove convergence of the error estimator with optimal algebraic rates, independently of the (coarse) initial mesh. As a technical contribution, we prove certain local inverse-type estimates for the boundary integral operators associated with the Helmholtz equation.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2018-07-31T13:19:05.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "optimal convergence rates",
      "helmholtz equation",
      "adaptive bem",
      "boundary integral operators",
      "3d helmholtz problem"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}