{
  "id": "2005.03349",
  "version": "v1",
  "published": "2020-05-07T09:25:45.000Z",
  "updated": "2020-05-07T09:25:45.000Z",
  "title": "Error estimates for the Cahn--Hilliard equation with dynamic boundary conditions",
  "authors": [
    "Paula Harder",
    "Balázs Kovács"
  ],
  "comment": "(preliminary version)",
  "categories": [
    "math.NA",
    "cs.NA"
  ],
  "abstract": "A proof of convergence is given for bulk--surface finite element semi-discretisation of the Cahn--Hilliard equation with Cahn--Hilliard-type dynamic boundary conditions in a smooth domain. The semi-discretisation is studied in the weak formulation as a second order system. Optimal-order uniform-in-time error estimates are shown in the $L^2$ and $H^1$ norms. The error estimates are based on a consistency and stability analysis. The proof of stability is performed in an abstract framework, based on energy estimates exploiting the anti-symmetric structure of the second order system. Numerical experiments illustrate the theoretical results.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-05-07T09:25:45.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "cahn-hilliard equation",
      "second order system",
      "bulk-surface finite element semi-discretisation",
      "cahn-hilliard-type dynamic boundary conditions",
      "optimal-order uniform-in-time error estimates"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}