A TWO-GRID MULTIPOINT FLUX MIXED FINITE ELEMENT METHOD FOR NONLINEAR PARABOLIC PROBLEMS

Wenwen Xu; Xindong Li; Nana Song; Lu Yang; Xiqian Yuan

doi:10.11948/20240209

2025 Volume 15 Issue 3

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Article navigation > Journal of Applied Analysis & Computation > 2025 > 15(3): 1310-1329

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Wenwen Xu, Xindong Li, Nana Song, Lu Yang, Xiqian Yuan. A TWO-GRID MULTIPOINT FLUX MIXED FINITE ELEMENT METHOD FOR NONLINEAR PARABOLIC PROBLEMS[J]. Journal of Applied Analysis & Computation, 2025, 15(3): 1310-1329. doi: 10.11948/20240209

Citation:

Wenwen Xu, Xindong Li, Nana Song, Lu Yang, Xiqian Yuan. A TWO-GRID MULTIPOINT FLUX MIXED FINITE ELEMENT METHOD FOR NONLINEAR PARABOLIC PROBLEMS[J]. Journal of Applied Analysis & Computation, 2025, 15(3): 1310-1329. doi: 10.11948/20240209

A TWO-GRID MULTIPOINT FLUX MIXED FINITE ELEMENT METHOD FOR NONLINEAR PARABOLIC PROBLEMS

1.
School of Mathematics and Statistics, Qilu University of Technology (Shandong Academy of Science), Jinan 250353, China

Author Bio: Email: wwxu@qlu.edu.cn(W. Xu); Email: songnana98@163.com(N. Song); Email: yanglu_roy@163.com(L. Yang); Email: xiqianyuann@163.com(X. Yuan)
Corresponding author: Email: lxd851268@126.com(X. Li)

Abstract

Abstract

This paper introduces a two-grid multipoint flux mixed finite element (MFMFE) method for solving nonlinear parabolic problems. The MFMFE method is advantageous due to its ability to decouple saddle point algebraic systems. The two-grid algorithm transforms nonlinear problems into smaller nonlinear systems on coarse grids and linear problems on fine grids, facilitating rapid decoupling of nonlinear equations. We present semi-discrete and fully discrete backward Euler schemes for the model problem. Theoretical results demonstrate the convergence order of velocity and pressure. A numerical example validates the effectiveness of the proposed algorithm, showing that the two-grid MFMFE method significantly reduces CPU running time compared to the standard MFMFE method.
- Nonlinear parabolic problems /
- multipoint flux mixed finite element /
- two-grid method /
- error estimates /
- numerical example
MSC: 65N12, 65N15, 65N30

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References

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