تقرير
A class of Discontinuous Galerkin methods for nonlinear variational problems
| العنوان: | A class of Discontinuous Galerkin methods for nonlinear variational problems |
|---|---|
| المؤلفون: | Grekas, Georgios, Koumatos, Konstantinos, Makridakis, Charalambos, Vikelis, Andreas |
| سنة النشر: | 2023 |
| المجموعة: | Computer Science Mathematics |
| مصطلحات موضوعية: | Mathematics - Numerical Analysis |
| الوصف: | In the context of Discontinuous Galerkin methods, we study approximations of nonlinear variational problems associated with convex energies. We propose element-wise nonconforming finite element methods to discretize the continuous minimisation problem. Using $\Gamma$-convergence arguments we show that the discrete minimisers converge to the unique minimiser of the continuous problem as the mesh parameter tends to zero, under the additional contribution of appropriately defined penalty terms at the level of the discrete energies. We finally substantiate the feasibility of our methods by numerical examples. |
| نوع الوثيقة: | Working Paper |
| URL الوصول: | http://arxiv.org/abs/2308.12891 |
| رقم الأكسشن: | edsarx.2308.12891 |
| قاعدة البيانات: | arXiv |
| الوصف غير متاح. |