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<p>In this paper, we investigate the finite element solutions for a variable exponent double phase problem, which, essentially, is a model relevant to various scientific and engineering applications, including electrorheological fluids. We begin by establishing the existence and uniqueness of the solution via using classical variational techniques. By constructing an appropriate energy functional, we reformulate the nonlinear partial differential equation as a minimization problem. This problem is then discretized using the finite element method, and we employ the quasi-Newton algorithm to find its solution. Finally, we validate the proposed method through several numerical examples, demonstrating its effectiveness across different variable exponent cases.</p>

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Finite element solutions for variable exponents double phase problems

  • 期刊论文

  • 发表日期：

    2025年8月1日

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  • Youness El Yazidi,
  • Abderrahim Charkaoui,
  • Shengda Zeng

摘要

In this paper, we investigate the finite element solutions for a variable exponent double phase problem, which, essentially, is a model relevant to various scientific and engineering applications, including electrorheological fluids. We begin by establishing the existence and uniqueness of the solution via using classical variational techniques. By constructing an appropriate energy functional, we reformulate the nonlinear partial differential equation as a minimization problem. This problem is then discretized using the finite element method, and we employ the quasi-Newton algorithm to find its solution. Finally, we validate the proposed method through several numerical examples, demonstrating its effectiveness across different variable exponent cases.