Exploiting Superconvergence in Discontinuous Galerkin Methods for Improved Time-Stepping and Visualization
Funded by European Office of Aerospace Research & Development, U.S. Air Force Office of Scientific Research, 2013
The discontinuous Galerkin (DG) method remains a popular choice in scientific computing due to its ability to flexibly handle complex geometries and high-order accuracy. However, its defining feature—permitting discontinuities between elements—poses significant computational and visualization challenges. The increased number of degrees of freedom enforces stricter time-stepping constraints, while the absence of smoothness across element boundaries complicates the use of standard visualization tools. Interestingly, DG methods exhibit superconvergence behavior, where unusually high accuracy is achieved at specific points or under special norms. This project aims to harness this superconvergence property to develop improved time integration strategies and design filters that enable smooth, precise visual representation of DG results, bridging the gap between numerical accuracy and practical usability.
Role:
Participated
Project Duration:
2013.02.01 – 2016.07.31
Funding:
European Office of Aerospace Research & Development,
U.S. Air Force Office of Scientific Research
Grant ID: FA8655-13-1-3017
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