Comparison of continuous and discontinuous finite element methods for parabolic differential equations employing implicit time integration. Issue 2 (4th May 2017)

• Record Type: Journal Article
• Authors: Rajaraman, P.; Vo, G. D.; Hansen, G.; Heys, J. J.
• Is Part Of: International journal for computational methods in engineering science and mechanics. Volume 18:Issue 2/3(2017)
• Page Start: 182
• Page End: 190
• Publication Date: 2017-05-04
• Subjects: Discontinuous Galerkin -- finite element method -- implicit integration -- interior penalty -- parabolic differential equations; Engineering -- Data processing -- Periodicals; Engineering mathematics -- Periodicals; Computer-aided engineering -- Periodicals; 620.00420285
• DOI: 10.1080/15502287.2017.1310150
• Languages: English
• ISSNs: 1550-2287

Abstract

ABSTRACT: This article compares the computational cost, stability, and accuracy of continuous and discontinuous Galerkin Finite Element Methods (GFEM) for various parabolic differential equations including the advection–diffusion equation, viscous Burgers' equation, and Turing pattern formation equation system. The results show that, for implicit time integration, the continuous GFEM is typically 5–20 times less computationally expensive than the discontinuous GFEM using the same finite element mesh and element order. However, the discontinuous GFEM is significantly more stable than the continuous GFEM for advection dominated problems and is able to obtain accurate approximate solutions for cases where the classic, un-stabilized continuous GFEM fails.