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arXiv · 2111.13267

The gradient discretisation method for the chemical reactions of biochemical systems

Yahya Alnashri·Hasan Alzubaidi
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Abstract

We consider a biochemical model that consists of a system of partial differential equations based on reaction terms and subject to non--homogeneous Dirichlet boundary conditions. The model is discretised using the gradient discretisation method (GDM) which is a framework covering a large class of conforming and non conforming schemes. Under classical regularity assumptions on the exact solutions, the GDM enables us to establish the existence of the model solutions in a weak sense, and strong convergence for the approximate solution and its approximate gradient. Numerical test employing a finite volume method is presented to demonstrate the behaviour of the solutions to the model.

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Yahya Alnashri, Hasan Alzubaidi. 2021-11-25. The gradient discretisation method for the chemical reactions of biochemical systems. https://arxiv.org/abs/2111.13267

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