Oberseminar Numerische Mathematik / Scientific Computing
JUN HU
School of Mathematical Sciences, Peking Univeristy, China
The Adaptive Finite Elemen Method for the Fourth Order Problem
Abstract:
For the fourth order elliptic problem, the use of conforming finite element methods often leads to very expensive calculations due to the fact that rather high polynomials are required to fulfill the C^1 continuity of the ansatz functions. Therefore, most of popular finite element methods in the literature are the nonconforming finite element method. There are a lot of papers concerning a priori analysis of the nonconforming finite elements in the literature. However, there are few works concerning the adaptive finite element methods of the fourth order problem. One difficulty is that all of nonconforming finite element spaces for the fourth order elliptic problems can not contain a conforming subspace that has the minimal approximation, which causes the challenge for the a posteriori error analysis of the nonconforming methods. Another difficulty is that most of conforming/nonconforming finite element spaces for the fourth order elliptic problems are nonnested on successive meshes. The latter is the main barrier for the convergence analysis of the adaptive finite element methods.
In this talk, we shall present some recent progress concerning the a posteriori error estimates of finite element methods for the Kirchhoff-Love plate problem and the convergence and optimality analysis of the corresponding adaptive algorithm. The result will go to the nonconforming Morley element and some conforming finite element methods. In addition, we will discuss state of art for this research field.
| Datum: | 06.02.12 | Zeit: | 18:00 Uhr | Ort: | FU Berlin, Institut für Mathematik, Arnimallee 6, 14195 Berlin. | Raum: | Raum 031 im Erdgeschoss |