{ "id": "1306.0377", "version": "v2", "published": "2013-06-03T12:27:49.000Z", "updated": "2014-11-21T14:48:44.000Z", "title": "Instance optimality of the adaptive maximum strategy", "authors": [ "Lars Diening", "Christian Kreuzer", "Rob Stevenson" ], "categories": [ "math.NA" ], "abstract": "In this paper, we prove that the standard adaptive finite element method with a (modified) `maximum marking strategy' is `instance optimal' for the `total error', being the sum of the energy error and the oscillation. This result will be derived in the model setting of Poisson's equation on a polygon, linear finite elements, and conforming triangulations created by newest vertex bisection.", "revisions": [ { "version": "v1", "updated": "2013-06-03T12:27:49.000Z", "comment": null, "journal": null, "doi": null }, { "version": "v2", "updated": "2014-11-21T14:48:44.000Z" } ], "analyses": { "subjects": [ "65N30", "65N12", "65N50", "65N15", "41A25" ], "keywords": [ "adaptive maximum strategy", "instance optimality", "standard adaptive finite element method", "newest vertex bisection", "linear finite elements" ], "note": { "typesetting": "TeX", "pages": 0, "language": "en", "license": "arXiv", "status": "editable", "adsabs": "2013arXiv1306.0377D" } } }