{
  "id": "2301.03172",
  "version": "v1",
  "published": "2023-01-09T05:13:19.000Z",
  "updated": "2023-01-09T05:13:19.000Z",
  "title": "Fully H(gradcurl)-nonconforming Finite Element Method for The Singularly Perturbed Quad-curl Problem on Cubical Meshes",
  "authors": [
    "Lixiu Wang",
    "Mingyan Zhang",
    "Qian Zhang"
  ],
  "categories": [
    "math.NA",
    "cs.NA"
  ],
  "abstract": "In this paper, we develop two fully nonconforming (both H(grad curl)-nonconforming and H(curl)-nonconforming) finite elements on cubical meshes which can fit into the Stokes complex. The newly proposed elements have 24 and 36 degrees of freedom, respectively. Different from the fully H(grad curl)-nonconforming tetrahedral finite elements in [9], the elements in this paper lead to a robust finite element method to solve the singularly perturbed quad-curl problem. To confirm this, we prove the optimal convergence of order $O(h)$ for a fixed parameter $\\epsilon$ and the uniform convergence of order $O(h^{1/2})$ for any value of $\\epsilon$. Some numerical examples are used to verify the correctness of the theoretical analysis.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2023-01-09T05:13:19.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "singularly perturbed quad-curl problem",
      "cubical meshes",
      "robust finite element method",
      "grad curl",
      "tetrahedral finite elements"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}