A Conforming Virtual Element Method for Solving the Pennes Bioheat Transfer Model on Polygonal Meshes

ABSTRACT This study investigates the Pennes bioheat transfer model within the framework of the Virtual Element Method, presenting for the first time its application as a computational approach to analyze the thermal behavior of biological tissues. The virtual element method, conceived as a natural extension of the finite element approach, is particularly advantageous for handling any type of complex meshes within the framework of Galerkin approximation. To ensure the robustness of this discretization technique, we establish the theoretical foundations of the model, including the derivation of optimal convergence rates, error estimates in the ‐norm, and proofs of existence and uniqueness of the discrete solution. A numerical investigation of the proposed scheme is conducted by applying it to the generalized bioheat transfer equation, discretized in time using Euler's method. A comparative analysis against the classical finite element method is carried out to rigorously evaluate the effectiveness of the proposed virtual element scheme. The results underscore the computational advantages of the virtual element method, demonstrating its ability to preserve accuracy and stability over complex mesh structures while providing deeper insights into the thermo‐regulatory mechanisms of biological tissues.