{
  "id": "2008.07186",
  "version": "v1",
  "published": "2020-08-17T10:02:54.000Z",
  "updated": "2020-08-17T10:02:54.000Z",
  "title": "On the convergence of adaptive stochastic collocation for elliptic partial differential equations with affine diffusion",
  "authors": [
    "Martin Eigel",
    "Oliver Ernst",
    "Björn Sprungk",
    "Lorenzo Tamellini"
  ],
  "comment": "20 pages",
  "categories": [
    "math.NA",
    "cs.NA"
  ],
  "abstract": "Convergence of an adaptive collocation method for the stationary parametric diffusion equation with finite-dimensional affine coefficient is shown. The adaptive algorithm relies on a recently introduced residual-based reliable a-posteriori error estimator. For the convergence proof, a strategy recently used for a stochastic Galerkin method with an hierarchical error estimator is transferred to the collocation setting.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-08-17T10:02:54.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "35R60",
      "65D05",
      "65D15",
      "65N12"
    ],
    "keywords": [
      "elliptic partial differential equations",
      "adaptive stochastic collocation",
      "affine diffusion",
      "reliable a-posteriori error estimator",
      "convergence"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 20,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}