Applied Mathematics Seminar

Department of Mathematics, University of Texas at Arlington

Date/Time/Room: Thursday (10/12/2000) at 3:30 pm in 487 Pickard Hall (Refreshments served at 3:00 pm)

Speaker: Peter Moore, Department of Mathematics, Southern Methodist University

``Interpolation error-based a posteriori estimation and applications to an h-adaptive refinement code for solving parabolic systems in three space dimensions''

Abstract: A posteriori error estimation plays a crucial role in adaptive methods for solving elliptic and parabolic equations using the finite element method. Babuska, Adjerid, Flaherty and Yu developed error estimates for odd order elements based on jumps in solution derivatives across element boundaries. Proofs of asymptotic exactness for these estimates depended on the fact that for a special interpolation polynomial, the interpolation error and finite element error are asymptotically equivalent. A different approach was necessary for even order elements. In my talk I will explain their results by finding a formula for the interpolation error. This formula leads to a new a posteriori error estimatator that holds for both odd and even order elements. I will discuss some implications for a posteriori estimation in three dimensions and present an h-adaptive algorithm that uses this estimate for solving parabolic systems in three space dimensions.