Computational Mathematics and Scientific Computing Seminar

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Superconvergence in Numerical Solutions: Making it Useful

Speaker: Jennifer Ryan, Delft University of Technology

Location: Warren Weaver Hall 1302

Date: April 13, 2012, 10 a.m.

Synopsis:

In this talk, I will discuss how to extract superconvergence from a given numerical solution. I will specifically focus on the discontinuous Galerkin method (DG), how superconvergence occurs for this method, and how to extract this "extra" theoretical information in a computationally efficient and useful manner. The main accuracy extraction technique is done using a Smoothness-Increasing Accuracy-Conserving (SIAC) filter. The interesting feature of this filter is that it overcomes smoothness issues of the DG solution by using information contained in the negative-order norm estimates to enhance the quality of the approximation in terms of both smoothness and accuracy. This requires visiting both the theoretical and computational aspects of accuracy enhancement and how this information can be exploited for applications such as in visualization.