Topics in Posteriori Error Estimations: Finite Element and Reduced Basis Methods

Catalog description

The course will contain two related parts. An introduction of different types of a posteriori error estimations for various finite element methods, certified reduced basis method, where a posteriori error estimations play an important role. Emphasize both the theory and implementation. Related Matlab programs. Residual-type, local-problem type, and recovery-type error estimators for conforming, mixed, non-conforming, and discontinuous galerkin finite element methods for different types of equations. Reduced basis methods, offline-online procedure, greedy algorithm, error estimator, empirical interpolation method, and successive constraint method will be discussed. Goal-Oriented primal-dual approach for both FEM and RBM will be covered. Objective: To learn various theoretical and practical results of adaptive finite element methods and reduced basis methods.