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A new nonconforming finite element method for convection dominated diffusion-reaction equations

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Abstract

In this article, we introduce a non-conforming streamline diffusion finite element method for the approximation of convection dominated diffusion problems. The proposed non-conforming scheme is a hybrid type in which \(P_{1}\)-nonconforming polynomials and \(P_{2}\)-conforming polynomials on triangles are used. Computational advantages of the newly constructed element with rigorous error analysis for the streamline diffusion discretization is presented. Moreover, numerical experiments are conducted to demonstrate the efficiency of the proposed scheme and to validate the theoretical error estimates.

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Authors and Affiliations

  1. Department of Mathematics, Indian Institute of Space Science and Technology, Thiruvananthapuram, Kerala, India

    Dibyendu Adak, E. Natarajan & Sarvesh Kumar

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  1. Dibyendu Adak
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  2. E. Natarajan
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  3. Sarvesh Kumar
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Correspondence to E. Natarajan.

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Adak, D., Natarajan, E. & Kumar, S. A new nonconforming finite element method for convection dominated diffusion-reaction equations. Int J Adv Eng Sci Appl Math 8, 274–283 (2016). https://doi.org/10.1007/s12572-016-0174-1

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  • DOI: https://doi.org/10.1007/s12572-016-0174-1

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