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Primal Hybrid Method For Quasilinear Parabolic Problems

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Abstract

In this article, a second order quasi-linear parabolic initial-boundary value problem is approximated by using primal hybrid finite element method and Lagrange multipliers. Semidiscrete and backward Euler based fully discrete schemes are discussed and optimal order error estimates are established by applying modified elliptic projection. Optimal order error estimates in maximum norm are also derived. Earlier results on maximum-norm superconvergence of the gradient in piecewise linear finite-element approximations of elliptic and parabolic problems are now carried over to quasilinear case using primal hybrid method. Finally, the results on numerical experiments confirm our theoretical findings.

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Data Availability

The codes during the current study are available from the corresponding author on reasonable request.

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Acknowledgements

The authors thank the anonymous referee for his/her valuable comments which help to improve the revised manuscript. The first and second authors acknowledge the financial support provided by the DST-FIST program (Govt. of India) for setting up the computing lab facility called Center for Mathematical & Financial Computing (C-MFC) at the LNM Institute of Information Technology under the scheme“Fund for Improvement of Science and Technology”(FIST - No. SR/FST/MS-I/2018/24).

Funding

The authors declare that no funds and grants were received during the preparation of this manuscript. However, the first and second authors acknowledge the computing lab facility provided by the“Center for Mathematical & Financial Computing (C-MFC)”at the LNM Institute of Information Technology supported financially by the DST-FIST program (Govt. of India) under the scheme“Fund for Improvement of Science and Technology” (FIST - No. SR/FST/MS-I/2018/24).

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Authors and Affiliations

  1. Department of Mathematics, The LNM Institute of Information Technology, Jaipur, Rajasthan, 302031, India

    Ravina Shokeen & Ajit Patel

  2. Department of Mathematics, Indian Institute of Technology Bombay, Powai, Mumbai, 400076, India

    Amiya K. Pani

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  1. Ravina Shokeen
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  2. Ajit Patel
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  3. Amiya K. Pani
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All authors contributed equally to prepare this manuscript. All authors read and approved the final manuscript.

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Correspondence to Amiya K. Pani.

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Shokeen, R., Patel, A. & Pani, A.K. Primal Hybrid Method For Quasilinear Parabolic Problems. J Sci Comput 92, 10 (2022). https://doi.org/10.1007/s10915-022-01858-z

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