Speaker:Ronald H.W. Hoppe, University of Houston/University of Augsburg
Title: Equilibrated A Posteriori Error Estimators for Interior Penalty Discontinuous Galerkin Approximations of Second and Fourth Order Elliptic Problems

Abstract: Interior Penalty Discontinuous Galerkin (IPDG) methods for second and fourth order elliptic boundary value problems can be derived from a mixed formu- lation of the problem involving properly specified numerical flux functions across interior faces of the underlying triangulation of the computational do- main. Equilibrated a posteriori error estimators can be derived by means of a two-energies principle also referred to as a hypercircle method or Prager- Synge theorem. The two-energies principle is based on the construction of an equilibrated flux for second order problems and an equilibrated moment tensor for fourth order problems. It results in a reliability estimate without generic constants except for possible data oscillations. On the other hand, the efficiency can be established by verifying that the estimators are bounded from above by residual-type a posteriori error estimators which are known to be efficient. The results are based on joint work with Dietrich Braess and Thomas Fraunholz.

Time: Friday, April 24, 2015, 1:30-2:30 p.m.

Place: Exploratory Hall, Room 4106

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