Session B6 - Multiresolution and Adaptivity in Numerical PDEs
July 15, 15:30 ~ 15:55 - Room T1
Mixed adaptive finite element discretization of linear elliptic equations in nondivergence form
Karlsruher Institut für Technologie, Germany - email@example.com
This talk discusses formulations of second-order elliptic partial differential equations in nondivergence form with Cordes coefficients on convex domains as equivalent variational problems. These formulations enable the use of standard finite element techniques for variational problems in subspaces of $H^2$ as well as mixed finite element methods from the context of fluid computations. Besides the immediate quasi-optimal a priori error bounds, the variational setting allows for a posteriori error control with explicit constants and adaptive mesh-refinement. The convergence of an adaptive algorithm is proved. Numerical results on uniform and adaptive meshes are included.