| Автор | Prohl, Andreas |
| Дата выпуска | 1999 |
| dc.description | The minimization of nonconvex functionals naturally arises in materials sciences where deformation gradients in certain alloys exhibit microstructures. For example, minimizing sequences of the nonconvex Ericksen-James energy can be associated with deformations in martensitic materials that are observed in experiments[2,3]. — From the numerical point of view, classical conforming and nonconforming finite element discretizations have been observed to give minimizers with their quality being highly dependent on the underlying triangulation, see [8,24,26,27] for a survey. Recently, a new approach has been proposed and analyzed in [15,16] that is based on discontinuous finite elements to reduce the pollution effect of a general triangulation on the computed minimizer. The goal of the present paper is to propose and analyze an adaptive method, giving a more accurate resolution of laminated microstructure on arbitrary grids. |
| Формат | application.pdf |
| Издатель | EDP Sciences |
| Копирайт | © EDP Sciences, SMAI, 1999 |
| Тема | Adaptive algorithm |
| Тема | finite element method |
| Тема | nonconvex minimization |
| Тема | multi-well problem |
| Тема | microstructure |
| Тема | multiscale |
| Тема | nonlinear elasticity |
| Тема | shape-memory alloy |
| Тема | materials science. |
| Название | An adaptive finite element method for solving a double well problem describing crystalline microstructure |
| Тип | research-article |
| DOI | 10.1051/m2an:1999163 |
| Electronic ISSN | 1290-3841 |
| Print ISSN | 0764-583X |
| Журнал | ESAIM: Mathematical Modelling and Numerical Analysis |
| Том | 33 |
| Первая страница | 781 |
| Последняя страница | 796 |
| Аффилиация | Prohl Andreas; Mathematisches Seminar, Christian-Albrechts-Universität Kiel, Ludewig-Meyn-Str. 4, 24098 Kiel, Germany. apr@numerik.uni-kiel.de. |
| Выпуск | 4 |
