A HYBRIDIZED CONTINUOUS/DISCONTINUOUS GALERKIN FORMULATION FOR STOKES PROBLEMWITH CONTINUOUS TRACE SPACE

Authors

  • Katia P. Fernandes Federal University of Rio de Janeiro
  • Webe João Mansur
  • Eduardo G.D. do Carmo

DOI:

https://doi.org/10.26512/ripe.v2i34.21813

Keywords:

Hybrid methods. Discontinuous Galerkin methods. Stokes problem.

Abstract

In this paper is presented a new hybridized continuous / discontinuous Galerkin formulation via continuous trace space for the Stokes problem. The method possesses unique features which distinguish itself from other methods. One of these features is that all the discontinuous variables are eliminated at element level as function of continuous trace variable, reducing thus the number of degrees of freedom and consequently the global system. Continuity and weak coercivity are presented in a suitable norm for the proposed formulation. Error estimates are also well established for velocity and pressure. Numerical experiments with the problem having smooth solution confirm the error estimates as well as the robustness of the formulation presented in this paper. Also, the numerical experiments with the classical cavity problem showed that the method presented here possesses a good ability for capturing the singularities of the pressure on the corners.

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References

Adams, R. A. (1975). Sobolev Spaces. New York: Academic Press.

Arnold, D. N., Brezzi, F., Cockburn, B., & Marini, L. D. (2001). Unified analysis of discontinuous galerkin methods for elliptic problems. SIAM J. Numer. Anal., 39, 1749”“1779.

Baumann, C. E., & Oden, J. T. (1999). A discontinuous hp finite element method for convectiondiffusion problems. Computer Methods in Applied Mechanics and Engineering, 175, 311”“ 341.

do Carmo, E. G. D., & Duarte, A. V. C. (2000). A discontinuous finite element-based domain decompositionmethod. Computer Methods in Applied Mechanics and Engineering, 190, 825”“ 843.

do Carmo, E. G. D., Fernandes, K. P., & Mansur, W. J. (submitted). A hybridized continuous/ discontinuous galerkin formulation for stokes problem with minimum global system. Computational and Applied Mathematics (submitted), .

do Carmo, E. G. D., Fernandes, M. A., & Mansur, W. J. (2015). Continuous/discontinuous galerkinmethods stabilized through transfer functions applied to the incompressible elasticity and to the stokes problem. Computer Methods in Applied Mechanics and Engineering, 283, 806 ”“ 840.

do Carmo, E. G. D., Fernandes, M. T. C. A., &Mansur,W. J. (2014). Continuous/discontinuous galerkin methods applied to elasticity problems. Computer Methods in Applied Mechanics and Engineering, 269, 291 ”“ 314.

Cockburn, B., Kanschat, G., & Schotzau, D. (2005). A locally conservative ldg method for the incompressible navier-stokes equation. Mathematics of Computation, 74, 1067 ”“ 1095.

Cockburn, B., Nguyen, J. G. N., Peraire, J., & Sayas, F. (2011). Analysis of hdg methods for stokes flow. Mathematics of Computation, 80, 723 ”“ 760.

Donea, J., & Huerta, A. (2003). Finite Element Methods for Flow Problems. (1st ed.). Wiley.

Egger, H., &Waluga, C. (2013). hp analysis of a hybrid dg method for stokes flow. IMA Journal of Numerical Analysis, (pp. 687”“721).

Ern, A., & Guermond, J.-L. (2004). Theory and Practice of Finite Elements. (1st ed.). New York: Springer.

Fortin,M. (1981). Old and new finite elements for incompressible flows. International Journal for Numerical Methods in Fluids, 1, 347”“364.

Hughes, T. J., Scovazzi, G., Bochev, P. B., & Buffa, A. (2006). A multiscale discontinuous galerkinmethod with the computational structure of a continuous galerkinmethod. Computer Methods in Applied Mechanics and Engineering, 195, 2761 ”“ 2787.

Nguyen, N., Peraire, J., & Cockburn, B. (2010). A hybridizable discontinuous galerkin method for stokes flow. Computer Methods in Applied Mechanics and Engineering, 199, 582 ”“ 597.

Reed, W. H., & Hill, T. R. (1973). Triangular mesh methods for the neutron transport equation. Los Alamos Scientific Laboratory, .

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Published

2017-08-07

How to Cite

P. Fernandes, K., Mansur, W. J., & G.D. do Carmo, E. (2017). A HYBRIDIZED CONTINUOUS/DISCONTINUOUS GALERKIN FORMULATION FOR STOKES PROBLEMWITH CONTINUOUS TRACE SPACE. Revista Interdisciplinar De Pesquisa Em Engenharia, 2(34), 104–124. https://doi.org/10.26512/ripe.v2i34.21813