컨텐츠 시작
학술대회/행사
초록검색
| 제출번호(No.) | 0589 |
|---|---|
| 분류(Section) | Invited Talk |
| 분과(Session) | Numerical Analysis / Scientific Computations / Mathematics in Science and Technology (SS-14) |
| 영문제목 (Title(Eng.)) |
On the asymptotic exactness of the error estimator for mixed finite element methods |
| 저자(Author(s)) |
Kwang-Yeon Kim1 Kangwon National University1 |
| 초록본문(Abstract) | Mixed finite element methods have been one of the popular choices for numerical approximation of second-order elliptic equations because they fulfill local mass conservation and allow accurate computation of the vector variable. One of their drawbacks is the relatively large size of the discrete algebraic systems compared with the primal methods of the same order, which makes it inevitable to apply adaptive mesh refinement based on a posteriori error estimators in order to keep as small number of degrees of freedom as possible in achieving a desired accuracy. Some a posteriori error estimators often exhibit amazing accuracy as the ratio of the estimated error to the actual error tends to unity when the mesh size goes to zero. In such cases we say that the error estimator is asymptotically exact. The purpose of this talk is to discuss the asymptotic exactness of the error estimator for the mixed finite element method proposed in [Alonso, Error estimators for a mixed method, Numer. Math. 74 (1996), 385--395]. The error estimator is based on solution of local problems which are similar to those of Bank and Weiser designed for the $P1$ conforming finite element method. It was established that the error estimator of Bank and Weiser is asymptotically exact on uniform meshes if the exact solution is $H^3$-regular, where the superconvergence property of the standard nodal interpolant is crucially exploited. By using a similar argument and the superconvergence property of the Fortin projection for the Raviart--Thomas element, we show that the error estimator of Alonso is asymptotically exact on uniform meshes if the vector solution is $H^2$-regular. We also carry out some numerical experiments to validate the theoretical results. |
| 분류기호 (MSC number(s)) |
65N30, 65N15 |
| 키워드(Keyword(s)) | a posteriori error estimator, asymptotic exactness, superconvergence, mixed finite element method |
| 강연 형태 (Language of Session (Talk)) |
English |