{
  "id": "2208.09969",
  "version": "v1",
  "published": "2022-08-21T21:43:37.000Z",
  "updated": "2022-08-21T21:43:37.000Z",
  "title": "Interior over-stabilized enriched Galerkin methods for second order elliptic equations",
  "authors": [
    "Jeonghun J. Lee",
    "Omar Ghattas"
  ],
  "categories": [
    "math.NA",
    "cs.NA"
  ],
  "abstract": "In this paper we propose a variant of enriched Galerkin methods for second order elliptic equations with over-stabilization of interior jump terms. The bilinear form with interior over-stabilization gives a non-standard norm which is different from the discrete energy norm in the classical discontinuous Galerkin methods. Nonetheless we prove that optimal a priori error estimates with the standard discrete energy norm can be obtained by combining a priori and a posteriori error analysis techniques. We also show that the interior over-stabilization is advantageous for constructing preconditioners robust to mesh refinement by analyzing spectral equivalence of bilinear forms. Numerical results are included to illustrate the convergence and preconditioning results.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2022-08-21T21:43:37.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "65N15",
      "65N30"
    ],
    "keywords": [
      "second order elliptic equations",
      "interior over-stabilized enriched galerkin methods",
      "discrete energy norm",
      "bilinear form",
      "interior over-stabilization"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}