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<p>In this work, we analyze the finite element discretization of a mathematical model describing cancer invasion with two cancer populations. The model consists of a system of partial differential equations that account for tumor cell movement, degradation of the extracellular matrix, and biochemical interactions with the surrounding environment. First, we study the existence of weak solutions. Then, we establish a priori error estimates for the finite element approximations, providing theoretical guarantees on the convergence and accuracy of the numerical solutions. Using energy estimates and functional analysis techniques, we derive bounds on the discretization error in appropriate Sobolev norms. Numerical experiments are presented to validate the theoretical findings and sensitivity analysis to explore the impact of nonlinear diffusion.</p>

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Error Estimates for Finite Element Discretizations of the Cancer Invasion Mathematical Model

  • 期刊论文

  • 发表日期：

    2026年2月9日

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  • J. Manimaran,
  • L. Shangerganesh,
  • A. Debbouche

摘要

In this work, we analyze the finite element discretization of a mathematical model describing cancer invasion with two cancer populations. The model consists of a system of partial differential equations that account for tumor cell movement, degradation of the extracellular matrix, and biochemical interactions with the surrounding environment. First, we study the existence of weak solutions. Then, we establish a priori error estimates for the finite element approximations, providing theoretical guarantees on the convergence and accuracy of the numerical solutions. Using energy estimates and functional analysis techniques, we derive bounds on the discretization error in appropriate Sobolev norms. Numerical experiments are presented to validate the theoretical findings and sensitivity analysis to explore the impact of nonlinear diffusion.