Department Home Page About Us: • Contact Info. • Faculty • Staff • Teaching Assistants Academic Program: • Admission • Undergraduate • Graduate • Certificates Courses: • Course Description • Class Web Pages • Class Syllabi Research: • Colloquium • Interdisciplinary Seminar • Seminars • Steve Goldman Lectures in Mathematical Physics Links: • Completing Online GEP Courses • Best Jobs • Newsletter • Math Lab •Math Placement Test • Careers • American Mathematical Society • Mathematical Association of America

Phone: (407) 823-6284;   Fax: (407) 823-6253;   MAP  207 2006-2007 MATHEMATICS COLLOQUIUM SERIES 02/08/07 Colloquium Dr. Dmitriy Leykekhman Rice University Recovered Gradient A Posteriori Error Estimators for Parabolic Problems Abstract:  A posteriori error estimates are important for the assessment ofthe quality of the computed solution to a partial differential equation (PDE) using the finite element method (FEM), as well as for adaptive mesh refinement. In this talk I will introduce a family of a posteriori error estimatorsthat have proven to be robust and that have been applied very successfully to thesolution of elliptic problems. These estimators are based on recovered gradients, a technique that uses averaging schemes to obtain better estimatesof the gradient of the PDE solution than are given by the gradient of the FEM approximation. Only recently, theoretical results have been obtained that explain the success of these a posteriori error estimators on non-structured meshes for elliptic problems. After discussing these results, I will outline the extension the recovered gradient estimators to parabolic problems and I will discuss limitations of these estimators.