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A weak Galerkin finite element method for singularly perturbed problems with two small parameters on Bakhvalov-type meshes

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Abstract

A weak Galerkin finite element method is proposed and analyzed for solving two-parameter singularly perturbed differential equations on Bakhvalov-type meshes. A robust optimal order convergence has been presented in the related energy and the balanced norms based on carefully defined penalization terms using piecewise higher order discontinuous functions in the interior of the mesh and single-valued zero order polynomial on the skeleton of the mesh. A special interpolation operator which deals with the difficulty arising from the standard interpolation error estimates on the Bakhvalov-type meshes is constructed. Finally, we give some numerical experiments to support theoretical results.

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Acknowledgements

The authors would like to express their deep gratitude to the editor and anonymous referees for their insightful comments and suggestions which have resulted in a stronger manuscript.

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Authors and Affiliations

  1. Artvin Vocational School, Accounting and Taxation, Artvin Çoruh University, Artvin, 08100, Turkey

    Suayip Toprakseven

  2. Department of Applied Mathematics, Delhi Technological University, Delhi, 110042, India

    Aditya Kaushik

  3. Department of Mathematics, Indraprastha College for Women, University of Delhi, Delhi, 110054, India

    Manju Sharma

Authors
  1. Suayip Toprakseven
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  2. Aditya Kaushik
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  3. Manju Sharma
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Contributions

Ş. Toprakseven and A. Kaushik wrote the main manuscript text and M. Sharma carried out the numerical experiments. All authors reviewed and revised the manuscript.

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Correspondence to Suayip Toprakseven.

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Toprakseven, S., Kaushik, A. & Sharma, M. A weak Galerkin finite element method for singularly perturbed problems with two small parameters on Bakhvalov-type meshes. Numer Algor 97, 727–751 (2024). https://doi.org/10.1007/s11075-023-01721-8

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  • DOI: https://doi.org/10.1007/s11075-023-01721-8

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