Adaptive discontinuous Galerkin methods for nonstationary convection-diffusion problems

作者：Cangiani Andrea^*; Georgoulis Emmanuil H; Metcalfe Stephen

来源：IMA Journal of Numerical Analysis, 2014, 34(4): 1578-1597.

DOI：10.1093/imanum/drt052

• discontinuous Galerkin
• unsteady convection-diffusion
• a posteriori error estimation
• adaptive finite element methods

This work is concerned with the derivation of a robust a posteriori error estimator for a discontinuous Galerkin (dG) method discretization of a linear nonstationary convection-diffusion initial/boundary value problem and with the implementation of a corresponding adaptive algorithm. More specifically, we derive a posteriori bounds for the error in the L-2(H-1) + L-infinity(L-2)-type norm for an interior penalty dG discretization in space and a backward Euler discretization in time. Finally, an adaptive algorithm is proposed utilizing the error estimator. Optimal rate of convergence of the adaptive algorithm is observed in a number of test problems and for various Peclet numbers.

• 出版日期2014-10