{"product_id":"9783834806642","title":"Advances in Numerical Mathematics","description":"\u003ch1\u003eAdvances in Numerical Mathematics\u003c\/h1\u003e \u003ch2\u003eSuttmeier, Franz-Theo\u003c\/h2\u003e \u003cp\u003eThis work describes a general approach to a posteriori error estimation and adaptive mesh design for ?nite element models where the solution is subjected to inequality constraints. This is an extension to variational inequalities of the so-called Dual-Weighted-Residual method (DWR method) which is based on a variational formulation of the problem and uses global duality arguments for deriving weighted a posteriori error estimates with respect to arbitrary functionals of the error. In these estimates local residuals of the computed solution are multiplied by sensitivity factors which are obtained from a - merically computed dual solution. The resulting local error indicators are used in a feed-back process for generating economical meshes which are tailored - cording to the particular goal of the computation. This method is developed here for several model problems. Based on these examples, a general concept is proposed, which provides a systematic way of adaptive error control for problems stated in form of variational inequalities. F¨ ur Alexandra, Katharina und Merle Contents 1 Introduction 1 2 Models in elasto-plasticity 13 2. 1 Governing equations . . . . . . . . . . . . . . . . . . . . . . . . 14 2. 2 Examples . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20 3 The dual-weighted-residual method 23 3. 1 A model situation in plasticity . . . . . . . . . . . . . . . . . . 24 3. 2 A posteriori error estimate . . . . . . . . . . . . . . . . . . . . . 25 3. 3 Evaluation of a posteriori error bounds . . . . . . . . . . . . . . 26 3. 4 Strategies for mesh adaptation . . . . . . . . . . . . . . . . . . 28 3. 5 Example . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30 4 Extensions to stabilised schemes 33 4. 1 Discretisation for themembrane-problem . . . . . . . . . . . . 35 4. 2 A posteriori error analysis . . . . . . . . . . . . . . . . . . . . . 37 4. 3 Numerical tests . . . . . . . . . . . . . . . . . . . . . . . . . . .\u003c\/p\u003e \u003ch3\u003eDetails\u003c\/h3\u003e \u003cp\u003ePublished by: Vieweg+Teubner Verlag\u003c\/p\u003e \u003cp\u003ePublication Date: 2008-08-28\u003c\/p\u003e \u003cp\u003eFormat: Paperback\u003c\/p\u003e \u003cp\u003eISBN-13: 9783834806642\u003c\/p\u003e \u003cp\u003eDOI: 10.1007\/978-3-8348-9546-2\u003c\/p\u003e \u003cp\u003eDimensions: 210cm x148cm\u003c\/p\u003e \u003cp\u003ePages: 161\u003c\/p\u003e ","brand":"Vieweg+Teubner Verlag","offers":[{"title":"Default Title","offer_id":45587000295564,"sku":"9783834806642","price":49.49,"currency_code":"USD","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0710\/9545\/1788\/files\/9783834806642.jpg?v=1775796029","url":"https:\/\/fh90cf-fv.myshopify.com\/products\/9783834806642","provider":"Late Knight Books and Services, LLC","version":"1.0","type":"link"}