Dr. S. K. Tomar

Johann Radon Institute for Computational and Applied Mathematics (RICAM), Austria

Functional a posteriori error estimates for discontinuous Galerkin approximations of elliptic problems

Abstract:

In this talk, functional a posteriori error estimates for discontinuous Galerkin (DG) approximations of elliptic type boundary value problems will be presented. These estimates, derived on purely functional grounds by the analysis of the respective differential problem, are based on a certain projection of DG approximations onto a conforming approximation in the energy space and then applying the functional a posteriori error estimates to the conforming approximation [1,2]. These estimates provide "guaranteed and computable" upper and lower bounds of the error in a broken norm. A number of numerical experiments will be presented which confirm the efficiency of the estimates.

References:[1] S. Repin, A posteriori error estimation for nonlinear variational problems by duality theory. Zapiski Nauchnych Semin. POMI, 243, 201-214 (1997)

[2] S. Repin, A posteriori error estimation for variational problems with uniformly convex functionals. Math. Comput., 69(230), 481-500 (2000)