{
  "id": "1912.07096",
  "version": "v1",
  "published": "2019-12-15T19:36:00.000Z",
  "updated": "2019-12-15T19:36:00.000Z",
  "title": "Dynamic and weighted stabilizations of the $L$-scheme applied to a phase-field model for fracture propagation",
  "authors": [
    "Christian Engwer",
    "Iuliu Sorin Pop",
    "Thomas Wick"
  ],
  "categories": [
    "math.NA",
    "cs.NA"
  ],
  "abstract": "We consider a phase-field fracture propagation model, which consists of two (nonlinear) coupled partial differential equations. The first equation describes the displacement evolution, and the second is a smoothed indicator variable, describing the crack position. We propose an iterative scheme, the so-called $L$-scheme, with a dynamic update of the stabilization parameters during the iterations. Our algorithmic improvements are substantiated with two numerical tests. The dynamic adjustments of the stabilization parameters lead to a significant reduction of iteration numbers in comparison to constant stabilization values.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2019-12-15T19:36:00.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "phase-field model",
      "weighted stabilizations",
      "phase-field fracture propagation model",
      "stabilization parameters",
      "coupled partial differential equations"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}