{
  "id": "2401.03672",
  "version": "v1",
  "published": "2024-01-08T05:45:45.000Z",
  "updated": "2024-01-08T05:45:45.000Z",
  "title": "Multiscale finite element method for Stokes-Darcy model",
  "authors": [
    "Yachen Hong",
    "Wenhan Zhang",
    "Lina Zhao",
    "Haibiao Zheng"
  ],
  "categories": [
    "math.NA",
    "cs.NA"
  ],
  "abstract": "This paper explores the application of the multiscale finite element method (MsFEM) to address steady-state Stokes-Darcy problems with BJS interface conditions in highly heterogeneous porous media. We assume the existence of multiscale features in the Darcy region and propose an algorithm for the multiscale Stokes-Darcy model. During the offline phase, we employ MsFEM to construct permeability-dependent offline bases for efficient coarse-grid simulation, with this process conducted in parallel to enhance its efficiency. In the online phase, we use the Robin-Robin algorithm to derive the model's solution. Subsequently, we conduct error analysis based on $L^2$ and $H^1$ norms, assuming certain periodic coefficients in the Darcy region. To validate our approach, we present extensive numerical tests on highly heterogeneous media, illustrating the results of the error analysis.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2024-01-08T05:45:45.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "multiscale finite element method",
      "construct permeability-dependent offline bases",
      "address steady-state stokes-darcy problems",
      "darcy region",
      "bjs interface conditions"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}