Discontinuous Galerkin method

From Wikipedia, the free encyclopedia

Discontinuous Galerkin methods (DG methods) form a class of numerical methods for solving partial differential equations. They combine features of the finite element and the finite volume framework and have been successfully applied to hyperbolic, elliptic and parabolic problems arising from a wide range of applications. DG methods have in particular received considerable interest for problems with a dominant first-order part, e.g. in electrodynamics and fluid mechanics.

Discontinuous Galerkin methods were first proposed and analyzed in the early 1970's as a technique to numerically solve partial differential equations. In 1973 Reed and Hill introduced a DG method to solve the hyperbolic neutron transport equation. The origin of the DG method for elliptic problems cannot be traced back to a single publication as features such as jump penalization in the modern sense where developed gradually. However, among the early influential contributors were Babuška, J.-L. Lions, Nitsche and Zlamal. A more complete account of the historical development and an introduction to DG methods for elliptic problems is given in a publication by Arnold, Brezzi, Cockburn and Marini.

[edit] See also

• Galerkin method
• Finite element method
• Finite volume method

[edit] References

• W.H. Reed and T.R. Hill, Triangular mesh methods for the neutron transport equation, Tech. Report LA-UR-73-479, Los Alamos Scientific Laboratory, 1973.
• D.N. Arnold, F. Brezzi, B. Cockburn and L.D. Marini, Unified analysis of discontinuous Galerkin methods for elliptic problems, SIAM J. Numer. Anal. 39(5):1749-1779, 2002.
• J.S. Hesthaven and T. Warburton, "Nodal Discontinuous Galerkin Methods: Algorithms, Analysis, and Applications". Springer Texts in Applied Mathematics 54. Springer Verlag, New York, 2008.