An  -local discontinuous Galerkin method for some quasilinear elliptic boundary value problems of nonmonotone type |
| |
| Authors: | Thirupathi Gudi Neela Nataraj Amiya K Pani |
| |
| Institution: | Department of Mathematics, Industrial Mathematics Group, Indian Institute of Technology Bombay, Powai, Mumbai-400076 ; Department of Mathematics, Industrial Mathematics Group, Indian Institute of Technology Bombay, Powai, Mumbai-400076 ; Department of Mathematics, Industrial Mathematics Group, Indian Institute of Technology Bombay, Powai, Mumbai-400076 |
| |
| Abstract: | In this paper, an  -local discontinuous Galerkin method is applied to a class of quasilinear elliptic boundary value problems which are of nonmonotone type. On  -quasiuniform meshes, using the Brouwer fixed point theorem, it is shown that the discrete problem has a solution, and then using Lipschitz continuity of the discrete solution map, uniqueness is also proved. A priori error estimates in broken  norm and  norm which are optimal in  , suboptimal in  are derived. These results are exactly the same as in the case of linear elliptic boundary value problems. Numerical experiments are provided to illustrate the theoretical results. |
| |
| Keywords: | $hp$-finite elements local discontinuous Galerkin method second order quasilinear elliptic problems error estimates order of convergence |
|
| 点击此处可从《Mathematics of Computation》浏览原始摘要信息 |
| 点击此处可从《Mathematics of Computation》下载免费的PDF全文 |
|
