lecture image Computational Mathematics Seminar Series
An Adaptive DG-θ Method with Residual-type Error Estimates for Linear Parabolic Problems
Natasha Sharma, University of Texas at El Paso
Assistant Professor
Digital Media Center 1034
February 03, 2015 - 03:30 pm

In this talk, we propose and analyze a fully discretized adaptive Discontinuous Galerkin-θ (DG-θ) method for linear parabolic problems with the space discretized by the DG finite elements and the time discretization realized by the popular θ-time stepping scheme. The a posteriori error analysis is based on the residual- type estimator derived by Verfu ̈rth for conforming approximations in space and θ-scheme in time. This DG-θ estimator will enable us to then realize the adaptive algorithm for local mesh refinement. The desirable properties of reliability and efficiency of the estimator will be then be discussed and finally, we will present numerical results to illustrate the performance of this method. 


Speaker's Bio:

Natasha Sharma earned her Ph.D. from University of Houston, Houston Texas in 2011 under the supervision of Prof. Ronald Hoppe. She then moved to Heidelberg, Germany to complete her postdoctoral research at the Interdisciplinary Center for Scientific Computing, Heidelberg University with Prof. Guido Kanschat. In Fall 2014, she joined the Department of Mathematical Sciences at University of Texas at El Paso as an assistant professor where she continues to pursue her research in the area of numerical methods to solve differential equations.

This lecture has refreshments @ 03:00 pm