Abstract
An analysis of the balance between the computational complexity, accuracy, and resolution requirements of a discontinuous Galerkin finite element method for the solution of the compressible Euler equations of gas dynamics is presented. The discontinuous Galerkin finite element method uses a very local discretization, which remains second order accurate on highly non-uniform meshes, but at the cost of an increase in computational complexity and memory use. The question of the balance between computational complexity and accuracy is addressed by studying the evolution of vortices in the wake of a wing. It is demonstrated that the discontinuous Galerkin finite element method on locally refined meshes can result in a significant reduction in computational cost.
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van der Ven, H., van der Vegt, J.J.W. (2000). Accuracy, Resolution, and Computational Complexity of a Discontinuous Galerkin Finite Element Method. In: Cockburn, B., Karniadakis, G.E., Shu, CW. (eds) Discontinuous Galerkin Methods. Lecture Notes in Computational Science and Engineering, vol 11. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-59721-3_45
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DOI: https://doi.org/10.1007/978-3-642-59721-3_45
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