{
  "id": "2403.18217",
  "version": "v1",
  "published": "2024-03-27T02:59:20.000Z",
  "updated": "2024-03-27T02:59:20.000Z",
  "title": "Mixed Variational Formulation of Coupled Plates",
  "authors": [
    "Jun Hu",
    "Zhen Liu",
    "Rui Ma",
    "Ruishu Wang"
  ],
  "categories": [
    "math.NA",
    "cs.NA"
  ],
  "abstract": "This paper proposes a mixed variational formulation for the problem of two coupled plates with a rigid {junction}. The proposed mixed {formulation} introduces {the union of} stresses and moments as {an auxiliary variable}, which {are} commonly of great interest in practical applications. The primary challenge lies in determining a suitable {space involving} both boundary and junction conditions of the auxiliary variable. The {theory} of densely defined operators in Hilbert spaces is employed to define {a nonstandard Sobolev space} without the use of trace operators. The well-posedness is established for the mixed formulation. Based on these conditions, this paper provides a framework {of} conforming {mixed} finite element methods. Numerical experiments are given to validate the theoretical results.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2024-03-27T02:59:20.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "mixed variational formulation",
      "coupled plates",
      "finite element methods",
      "nonstandard sobolev space",
      "primary challenge lies"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}