Implicit–Explicit Backward Difference Formulae Discontinuous Galerkin Finite Element Methods for Convection–Diffusion Problems

Miloslav Vlasák () and Vít Dolejší ()
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Miloslav Vlasák: Charles University Prague, Faculty of Mathematics and Physics
Vít Dolejší: Charles University Prague, Faculty of Mathematics and Physics

A chapter in Numerical Mathematics and Advanced Applications 2009, 2010, pp 921-928 from Springer

Abstract: Abstract We deal with a numerical solution of a scalar nonstationary convection–diffusion equation with a nonlinear convection and a linear diffusion. We carry out the space semi-discretization with the aid of the symmetric interior penalty Galerkin (SIPG) method and the time discretization by backward difference formulae (BDF) and suitable linearization of nonlinear convective term. The resulting scheme is unconditionally stable, has a high order of accuracy with respect to space and time coordinates and requires solutions of linear algebraic problems at each time step. We derive a priori error estimates in the L ∞ (L 2)-norm up to the order 6 in time.

Keywords: Weak Solution; Diffusion Equation; Discontinuous Galerkin; Diffusion Problem; Discontinuous Galerkin Method (search for similar items in EconPapers)
Date: 2010
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-642-11795-4_99

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DOI: 10.1007/978-3-642-11795-4_99

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