Adaptive backward difference formula - Discontinuous Galerkin finite element method for the solution of conservation laws

0360357 - MÚ 2012 GB eng J - Článek v odborném periodiku
Dolejší, V. - Kůs, Pavel
Adaptive backward difference formula - Discontinuous Galerkin finite element method for the solution of conservation laws.
International Journal for Numerical Methods in Engineering. Roč. 73, č. 12 (2008), s. 1739-1766. ISSN 0029-5981. E-ISSN 1097-0207
Klíčová slova: backward difference formula * discontinuous Galerkin method * adaptive choice of the time step
Kód oboru RIV: BA - Obecná matematika
Impakt faktor: 2.229, rok: 2008
http://onlinelibrary.wiley.com/doi/10.1002/nme.2143/abstract

We deal with the numerical solution of the system of conservation laws. Although this approach has been proposed for a simulation of inviscid compressible flow, it can be straightforwardly applied to more general problems. We carried out the space semi-discretization by the discontinuous Galerkin finite element (DGFE) method, which is based on a piecewise polynomial discontinuous approximation. The resulting system of ordinary differential equations is discretized by the backward difference formula (BDF). A suitable linearization of the physical fluxes leads to a scheme that is practically unconditionally stable and has a higher order of accuracy with respect to the space and time coordinates and we solve a linear algebraic system at each time level. Moreover, we develop an adaptive technique for a choice of the length of the time step that is based on the use of two BDFs of the same order of accuracy. We call the resulting scheme the ABDF-DGFE (adaptive BDF-DGFE) method.
Trvalý link: http://hdl.handle.net/11104/0197928