{
  "id": "2212.12448",
  "version": "v1",
  "published": "2022-12-23T16:21:40.000Z",
  "updated": "2022-12-23T16:21:40.000Z",
  "title": "Mixed and multipoint finite element methods for rotation-based poroelasticity",
  "authors": [
    "Wietse M. Boon",
    "Alessio Fumagalli",
    "Anna Scotti"
  ],
  "categories": [
    "math.NA",
    "cs.NA"
  ],
  "abstract": "This work proposes a mixed finite element method for the Biot poroelasticity equations that employs the lowest-order Raviart-Thomas finite element space for the solid displacement and piecewise constants for the fluid pressure. The method is based on the formulation of linearized elasticity as a weighted vector Laplace problem. By introducing the solid rotation and fluid flux as auxiliary variables, we form a four-field formulation of the Biot system, which is discretized using conforming mixed finite element spaces. The auxiliary variables are subsequently removed from the system in a local hybridization technique to obtain a multipoint rotation-flux mixed finite element method. Stability and convergence of the four-field and multipoint mixed finite element methods are shown in terms of weighted norms, which additionally leads to parameter-robust preconditioners. Numerical experiments confirm the theoretical results.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2022-12-23T16:21:40.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "65N12",
      "65N22",
      "65N30"
    ],
    "keywords": [
      "mixed finite element method",
      "multipoint finite element methods",
      "rotation-flux mixed finite element",
      "rotation-based poroelasticity",
      "mixed finite element spaces"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}