{
  "id": "2103.07288",
  "version": "v1",
  "published": "2021-03-12T14:04:20.000Z",
  "updated": "2021-03-12T14:04:20.000Z",
  "title": "Energy stable and accurate coupling of finite element methods and finite difference methods",
  "authors": [
    "Tuan Anh Dao",
    "Ken Mattsson",
    "Murtazo Nazarov"
  ],
  "categories": [
    "math.NA",
    "cs.NA"
  ],
  "abstract": "We introduce a hybrid method to couple continuous Galerkin finite element methods and high-order finite difference methods in a nonconforming multiblock fashion. The aim is to optimize computational efficiency when complex geometries are present. The proposed coupling technique requires minimal changes in the existing schemes while maintaining strict stability, accuracy, and energy conservation. Results are demonstrated on linear and nonlinear scalar conservation laws in two spatial dimensions.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2021-03-12T14:04:20.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "34A45",
      "G.1.8"
    ],
    "keywords": [
      "energy stable",
      "accurate coupling",
      "high-order finite difference methods",
      "couple continuous galerkin finite element",
      "nonlinear scalar conservation laws"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}