Abstract
In this paper we present a new idea to stabilize Continuous Galerkin Schemes on grids with hanging nodes by using Discontinuous Galerkin (DG) approximations. We derive an a posteriori error estimate for a class of DG schemes including the CDG and CDG2 methods and apply this to standard test cases for CG methods such a the reentrant corner.
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References
Arnold, D., Brezzi, F., Cockburn, B., Marini, L.: Unified analysis of discontinuous Galerkin methods for elliptic problems. SIAM J. Numer. Anal. 39(5), 1749–1779 (2002)
Bangerth, W., Hartmann, R., Kanschat, G.: deal.II—a general purpose object oriented finite element library. ACM Trans. Math. Softw. 33(4), 24/1–24/27 (2007)
Bastian, P., Birken, K., Johannsen, K., Lang, S., Neuss, N., Rentz-Reichert, H., Wieners, C.: UG—a flexible software toolbox for solving partial differential equations. Comput. Vis. Sci. 1, 27–40 (1997)
Brdar, S., Dedner, A., Klöfkorn, R.: Compact and stable Discontinuous Galerkin methods for convection-diffusion problems. SIAM J. Sci. Comput. 34(1), 263–282. http://dx.doi.org/10.1137/100817528 (2012)
Houston, P., Schötzau, D., Wihler, T.: Energy norm a posteriori error estimation for mixed discontinuous Galerkin approximations of the Stokes problem. J. Sci. Comput. 22–23, 347–370 (2005)
Johnson, C.: Numerical solution of partial differential equations by the finite element method. Acta Applicandae Mathematica 18(2), 184–186 (1990)
Schmidt, A., Siebert, K.: Design of Adaptive Finite Element Software—the Finite Element Toolbox ALBERTA. Springer, Heidelberg (2005)
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Dedner, A., Klöfkorn, R., Kränkel, M. (2014). Continuous Finite-Elements on Non-Conforming Grids Using Discontinuous Galerkin Stabilization. In: Fuhrmann, J., Ohlberger, M., Rohde, C. (eds) Finite Volumes for Complex Applications VII-Methods and Theoretical Aspects. Springer Proceedings in Mathematics & Statistics, vol 77. Springer, Cham. https://doi.org/10.1007/978-3-319-05684-5_19
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DOI: https://doi.org/10.1007/978-3-319-05684-5_19
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