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Expanded mixed FEM with lowest order RT elements for nonlinear and nonlocal parabolic problems

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Abstract

In this paper, an expanded mixed finite element method with lowest order Raviart Thomas elements is developed and analyzed for a class of nonlinear and nonlocal parabolic problems. After obtaining some regularity results for the exact solution, a priori error estimates for the semidiscrete problem are established. Based on a linearized backward Euler method, a complete discrete scheme is proposed and a variant of Brouwer’s fixed point theorem is used to derive an existence of a fully discrete solution. Further, a priori error estimates for the fully discrete scheme are established. Finally, numerical experiments are conducted to confirm our theoretical findings.

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Acknowledgments

The authors thank the two anonymous referees for their suggestions and comments.The second author acknowledges the support provided by IIT Bombay vide IRCC project No.13IRAWD007. The first author acknowledges the support given by the National Program on Differential Equations: Theory, Computation and Applications (NPDE-TCA) vide the DST project No.SR/S4/MS:639/90.

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Authors and Affiliations

  1. Department of Mathematics, MCM DAV College for Women, Sector 36-A, Chandigarh, 160036, India

    Nisha Sharma

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

    Amiya K. Pani

  3. Department of Mathematics, South Asian University, New Delhi, 110021, India

    Kapil K. Sharma

Authors
  1. Nisha Sharma
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  2. Amiya K. Pani
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  3. Kapil K. Sharma
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Correspondence to Kapil K. Sharma.

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Communicated by: Paul Houston

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Sharma, N., Pani, A.K. & Sharma, K.K. Expanded mixed FEM with lowest order RT elements for nonlinear and nonlocal parabolic problems. Adv Comput Math 44, 1537–1571 (2018). https://doi.org/10.1007/s10444-018-9596-6

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  • DOI: https://doi.org/10.1007/s10444-018-9596-6

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