Some advances of nonconforming finite element methods for fourth-order singularly perturbation problems

by Shudan Tian (Xiangtan University)

Thursday 20 Jun 2024, 13:00 → 14:00 Europe/Berlin

R 3517 (Ernst-Abbe-Platz 2)

This talk will present a residual-based error estimator  of fourth-order singularly perturbation problems applicable to many existing H2 nonconforming elements.  
The error estimator involves the local best-approximation error of the finite element function by piecewise polynomial functions of the degree determining the expected approximation order, which need not coincide with the maximal polynomial degree of the element, for example if bubble functions are used. The error estimator is shown to be reliable and locally efficient up to this polynomial best-approximation error and oscillations of the right-hand side.

Then I will introduce some new finite element mehods for linear strain graident elastic model, which is also a fourth order singularly perturbation problem and can be viewed as an extension of linear elastic. These new methods are shown to be robust in handling both elastic and singular parameters.