A two-grid method for discontinuous Galerkin approximations to nonlinear Sobolev equations

Abstract

A two-grid algorithm for discontinuous Galerkin approximations to nonlinear Sobolev equations is proposed. H1 norm error estimate of the two-grid method for the nonlinear parabolic problem is derived. The analysis shows that our two-grid discontinuous Galerkin algorithm will achieve asymptotically optimal approximation as long as the mesh sizes satisfy \(h = O(H^{\frac {r+1}{r}})\), where r is the order of the discontinuous finite element space. The numerical experiments are presented to prove the efficiency of our algorithm.

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Funding

This work was supported by Hunan Provincial Natural Science Foundation of China (Grant No. 2020JJ4242, 2019JJ50105).

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Correspondence to Jiming Yang.

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Yang, J., Zhou, J. A two-grid method for discontinuous Galerkin approximations to nonlinear Sobolev equations. Numer Algor (2020). https://doi.org/10.1007/s11075-020-00943-4

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Keywords

  • Two-grid
  • Discontinuous Galerkin method
  • Sobolev equations

Mathematics subject classification (2010)

  • 65M12
  • 65M60