Implementation of the continuous-discontinuous Galerkin finite element method

Cangiani, Andrea, Chapman, John, Georgoulis, Emmanuil and Jensen, Max (2013) Implementation of the continuous-discontinuous Galerkin finite element method. In: Cangiani, Andrea, Davidchack, Ruslan, Georgoulis, Emmanuil, Gorban, Alexander, Levesley, Jeremy and Tretyakov, Michael (eds.) Numerical mathematics and advanced applications 2011: proceedings of ENUMATH 2011, the 9th European Conference on Numerical Mathematics and Advanced Applications, Leicester, September 2011. Springer, Berlin, pp. 315-322. ISBN 9783642331336

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For the stationary advection-diffusion problem the standard continuous Galerkin method is unstable without some additional control on the mesh or method. The interior penalty discontinuous Galerkin method is more stable but at the expense of an increased number of degrees of freedom. The hybrid method proposed in [5] combines the computational complexity of the continuous method with the stability of the discontinuous method without a significant increase in degrees of freedom. We discuss the implementation of this method using the finite element library deal.ii and present some numerical experiments.

Item Type: Book Section
Schools and Departments: School of Mathematical and Physical Sciences > Mathematics
Subjects: Q Science > QA Mathematics > QA0297 Numerical analysis
Depositing User: Max Jensen
Date Deposited: 19 Jun 2013 11:48
Last Modified: 22 Feb 2016 12:14
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