Fully discrete stabilized multiphysics finite element method for the polymer gel model. (15th July 2018)

• Record Type: Journal Article
• Authors: Ge, Zhihao; Guan, Zhen; He, Yinnian
• Is Part Of: Computers & mathematics with applications. Volume 76:issue 2(2018)
• Page Start: 393
• Page End: 405
• Publication Date: 2018-07-15
• Subjects: Polymer gel model -- Multiphysics finite element method -- Stabilized method; Electronic data processing -- Periodicals; Mathematics -- Data processing -- Periodicals; 510.28541
• DOI: 10.1016/j.camwa.2018.04.025
• Languages: English
• ISSNs: 0898-1221

Abstract

Abstract: In this paper, we propose a fully discrete stabilized multiphysics finite element method by the pressure projection method to solve the polymer gel model. To reveal the multi-physical process of the polymer gel model, we reformulate the polymer gel model by introducing a new variable to get a new multi-field problem, then we propose the fully discrete stabilized multiphysics finite element method using the simplest equal order element of P 1 − P 1 − P 1 without the discrete inf–sup condition to solve the new reformulated system, and we prove that the new method not only has no "locking" phenomenon, but also preserves some energy conservation laws. Also, we prove that the stabilized multiphysics finite element method has optimal convergence order. Finally, we give the numerical example to verify the theoretical results.