Mathematics Winter School 

14/03/2024, 11:00 — 11:15 — Room P3.10, Mathematics Building Online
Juha Videman, Instituto Superior Técnico

Adaptive Finite Elements for Contact Problems

Contact problems are of great engineering interest and they occur in numerous areas of physics and mechanics, think, for example, of a contact between two elastic bodies. In mathematical terms, these problems are expressed as variational inequalities and most often approximated by the finite element method. However, because the contact region is normally not known in advance, it is difficult to approximate the problem accurately without resorting to an adaptive mesh refinement. Adaptive finite elements use less degrees-of-freedom than uniform meshes to achieve a given accuracy and whereas the convergence rate of the uniform strategy is limited by the regularity of the exact solution, the adaptive strategy successfully regains the optimal convergence rate. Here, we introduce some elementary ideas of adaptivity through a number of contact problems.

See also

11H00_JV.pdf