### Applied Mathematics Seminar

Department of Mathematics, University of Texas at Arlington

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__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.