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2023, Volume 31, Issue 12: 7207-7223. doi: 10.3934/era.2023365
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Research article

Two-grid $ H^1 $-Galerkin mixed finite elements combined with $ L1 $ scheme for nonlinear time fractional parabolic equations

  • 1.
    School of Foundation Studies, Zhejiang Pharmaceutical University, Ningbo 315500, China
  • 2.
    College of Science, Hunan University of Science and Engineering, Yongzhou 425199, China

  • Academic Editor: Alain Miranville
  • Received: 08 September 2023 Revised: 27 October 2023 Accepted: 07 November 2023 Published: 10 November 2023

  • In this paper, we propose a two-grid algorithm for nonlinear time fractional parabolic equations by $ H^1 $-Galerkin mixed finite element discreitzation. First, we use linear finite elements and Raviart-Thomas mixed finite elements for spatial discretization, and $ L1 $ scheme on graded mesh for temporal discretization to construct a fully discrete approximation scheme. Second, we derive the stability and error estimates of the discrete scheme. Third, we present a two-grid method to linearize the nonlinear system and discuss its stability and convergence. Finally, we confirm our theoretical results by some numerical examples.

    Citation: Jun Pan, Yuelong Tang. Two-grid $ H^1 $-Galerkin mixed finite elements combined with $ L1 $ scheme for nonlinear time fractional parabolic equations[J]. Electronic Research Archive, 2023, 31(12): 7207-7223. doi: 10.3934/era.2023365

    Related Papers:

  • In this paper, we propose a two-grid algorithm for nonlinear time fractional parabolic equations by $ H^1 $-Galerkin mixed finite element discreitzation. First, we use linear finite elements and Raviart-Thomas mixed finite elements for spatial discretization, and $ L1 $ scheme on graded mesh for temporal discretization to construct a fully discrete approximation scheme. Second, we derive the stability and error estimates of the discrete scheme. Third, we present a two-grid method to linearize the nonlinear system and discuss its stability and convergence. Finally, we confirm our theoretical results by some numerical examples.


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