A Priori Error Estimates of an Extrapolated Space-Time Discontinuous Galerkin Method for Nonlinear Convection-Diffusion Problems

作者：V****k M; Dolejsi V^*; Hajek J

来源：Numerical Methods for Partial Differential Equations, 2011, 27(6): 1456-1482.

DOI：10.1002/num.20591

• a priori error estimates
• experimental order of convergence
• nonlinear convection-diffusion equation
• semi-implicit scheme
• space-time discontinuous Galerkin finite element method

We deal with the numerical solution of a scalar nonstationary nonlinear convection-diffusion equation. We employ a combination of the discontinuous Galerkin finite element (DGFE) method for the space as well as time discretization. The linear diffusive and penalty terms are treated implicitly whereas the nonlinear convective term is treated by a special higher order explicit extrapolation from the previous time step, which leads to the necessity to solve only a linear algebraic problem at each time step. We analyse this scheme and derive a priori asymptotic error estimates in the L-infinity(L-2)-norm and the L-2(H-1)-seminorm with respect to the mesh size h and time step tau. Finally, we present an efficient solution strategy and numerical examples verifying the theoretical results.

• 出版日期2011-11