Visualization of Discontinuous Galerkin Based High-Order Methods
University of Utah Salt Lake City
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The discontinuous Galerkin method DGM has become, in recent times, one of the most widely researched and utilized discretization methodologies for solving problems in science and engineering. Fundamentally based upon the mathematical framework of variational methods, the DG methodology provides hope that computationally fast, efficient and robust methods can be constructed for solving real-world problems. Through a combination of a dual path to convergence allowing naturally both conforming and non-conforming hanging node non-overlapping discretizations of the solution domain combined with possibly non-uniform polynomial enrichment also known as p-refinement the DG methodology provides a rich mathematical starting point for the development of domain specific solvers. By not requiring that the solution be continuous across element boundaries, the DGM provides a flexibility that can be exploited both for geometric and solution adaptivity and for parallelization.
- Numerical Mathematics