Acta mathematica scientia, Series B >

2026 , Vol. 46 >Issue 2: 1011 - 1035

DOI: https://doi.org/10.1007/s10473-026-0225-z

PRIMAL HYBRID FINITE ELEMENT METHOD FOR PARABOLIC PROBLEMS WITH GRADIENT TYPE NON-LINEARITY

  • Ravina SHOKEEN ,
  • Ajit PATEL ,
  • Divay GARG
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  • 1. Department of Applied Science and Humanities, World College of Technology and Management, Farukh Nagar, Gurgaon, Haryana 122506, India;
    2. Department of Mathematics,The LNM Institute of Information Technology, Jaipur, Rajasthan 302031, India;
    3. Department of Applied Science, Galgotias College of Engineering and Technology, Knowledge Park-II, Greater Noida, G.B. Nagar, U.P. 201310, India
Ravina SHOKEEN, E-mail: ravinashokeen@outlook.com; Divay GARG, E-mail: divaygarg2@gmail.com

Received date: 2023-11-20

  Revised date: 2024-01-08

  Online published: 2026-05-22

Supported by

The first two 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). The third author is supported by CSIR research fellowship.

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Abstract

This article develops the primal hybrid finite element method with Lagrange multipliers to approximate nonlinear parabolic initial-boundary value problems with gradient type non-linearity.A modified elliptic projection is used to produce optimal order error estimates for the semi-discrete and backward Euler-based complete discrete schemes. In addition, error estimates in $L^{\infty}$-norm are established which are optimal in nature. Superconvergence result of the gradient in $L^{\infty}$-norm is discussed for the error between the primal hybrid solution and elliptic projection. As a bi-product, the proposed analysis provides optimal error analysis for non-conforming CR-elements.Finally, numerical tests are performed to validate the theoretical findings.

Key words： primal hybrid method (PHM); modified elliptic projection; strongly non-linear parabolic problem; semi-discrete method; Lagrange multiplier; complete discrete method; numerical results

Cite this article

Ravina SHOKEEN , Ajit PATEL , Divay GARG . PRIMAL HYBRID FINITE ELEMENT METHOD FOR PARABOLIC PROBLEMS WITH GRADIENT TYPE NON-LINEARITY[J]. Acta mathematica scientia, Series B, 2026 , 46(2) : 1011 -1035 . DOI: 10.1007/s10473-026-0225-z

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