{
  "id": "2209.08405",
  "version": "v1",
  "published": "2022-09-17T21:18:58.000Z",
  "updated": "2022-09-17T21:18:58.000Z",
  "title": "A Steklov-spectral approach for solutions of Dirichlet and Robin boundary value problems",
  "authors": [
    "Kthim Imeri",
    "Nilima Nigam"
  ],
  "categories": [
    "math.NA",
    "cs.NA",
    "math.AP",
    "math.SP"
  ],
  "abstract": "In this paper we revisit an approach pioneered by Auchmuty to approximate solutions of the Laplace- Robin boundary value problem. We demonstrate the efficacy of this approach on a large class of non-tensorial domains, in contrast with other spectral approaches for such problems. We establish a spectral approximation theorem showing an exponential fast numerical evaluation with regards to the number of Steklov eigenfunctions used, for smooth domains and smooth boundary data. A polynomial fast numerical evaluation is observed for either non-smooth domains or non-smooth boundary data. We additionally prove a new result on the regularity of the Steklov eigenfunctions, depending on the regularity of the domain boundary. We describe three numerical methods to compute Steklov eigenfunctions.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2022-09-17T21:18:58.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "35R30",
      "35C20"
    ],
    "keywords": [
      "robin boundary value problem",
      "steklov-spectral approach",
      "steklov eigenfunctions",
      "smooth boundary data",
      "exponential fast numerical evaluation"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}