Details

Autor(en) / Beteiligte

• CHENG, YINGDA
• SHU, CHI-WANG

Titel

SUPERCONVERGENCE OF DISCONTINUOUS GALERKIN AND LOCAL DISCONTINUOUS GALERKIN SCHEMES FOR LINEAR HYPERBOLIC AND CONVECTION-DIFFUSION EQUATIONS IN ONE SPACE DIMENSION

Ist Teil von

• SIAM journal on numerical analysis, 2010-01, Vol.47 (6), p.4044-4072

Ort / Verlag

Philadelphia: Society for Industrial and Applied Mathematics

Erscheinungsjahr

2010

Quelle

Alma/SFX Local Collection

Beschreibungen/Notizen

• In this paper, we study the superconvergence property for the discontinuous Galerkin (DG) and the local discontinuous Galerkin (LDG) methods for solving one-dimensional time dependent linear conservation laws and convection-diffusion equations. We prove superconvergence towards a particular projection of the exact solution when the upwind flux is used for conservation laws and when the alternating flux is used for convection-diffusion equations. The order of superconvergence for both cases is proved to be $k+\frac{3}{2}$ when piecewise P k polynomials with k ≥ 1 are used. The proof is valid for arbitrary nonuniform regular meshes and for piecewise P k polynomials with arbitrary k ≥ 1, improving upon the results in [Y. Cheng and C.-W. Shu, J. Comput. Phys., 227 (2008), pp. 9612—9627], [Y. Cheng and C.-W. Shu, Computers and Structures, 87 (2009), pp. 630—641] in which the proof based on Fourier analysis was given only for uniform meshes with periodic boundary condition and piecewise P¹ polynomials.