DEPARTMENT OF MATHEMATICAL SCIENCES

APPLIED AND COMPUTATIONAL MATHEMATICS SEMINAR

**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

Department of Mathematical Sciences

George Mason University

4400 University Drive, MS 3F2

Fairfax, VA 22030-4444

http://math.gmu.edu/

Tel. 703-993-1460, Fax. 703-993-1491