Error analysis of a two-grid discontinuous Galerkin method for non-linear parabolic equations

Abstract

Discontinuous Galerkin (DG) approximations for non-linear parabolic problems are investigated. To linearize the discretized equations, we use a two-grid method involving a small non-linear system on a coarse gird of size H and a linear system on a fine grid of size h. Error estimates in H¹-norm are obtained, O(h^r+H^r+1) where r is the order of the DG space. The analysis shows that our two-grid DG algorithm will achieve asymptotically optimal approximation as long as the mesh sizes satisfy h=O(H^(r+1)/r). The numerical experiments verify the efficiency of our algorithm.

Keywords:

• two-grid
• discontinuous Galerkin method
• error estimate

1991 AMS Subject Classifications:

• 65M12
• 65M60

Disclosure Statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

This work was supported by project funded by China Postdoctoral Science Foundation [grant number 2014M562117], Scientific Research Fund of Hunan Provincial Education Department [grant number 14A034], the Planned Science and Technology Project of Hunan Province [grant number 2014FJ4258], Zhejiang Provincial Natural Science Foundation of China [grant number LQ13A010019], National Natural Science Foundation of China [grant number 11172100].