Mesh Refinement Compensation via Regression in thermal necrosis FEM

Abstract Finite Element Models (FEM) for simulating various physical phenomena are indispensable in today’s research. They are also applied in high-frequency (HF) surgical applications to simulate Joule heating and thermal necrosis formation in biological tissue. One challenge lies in choosing an appropriate mesh size, balancing between sufficiently accurate simulation results and a coarse mesh for fast computations. In this contribution, we investigate, using three mesh sizes (coarse, medium, and fine), the extent to which regression analysis of discrete simulation results of necrosis dimensions can compensate for mesh refinement in an FEM for HF soft coagulation. We conducted exponential regression analysis on discrete simulation results of the necrosis zone. It has been found that while it is generally possible, if the FEM simulation results already deviate significantly from the true solution, regression analysis cannot compensate for errors arising from the numerical method. Therefore, a coarse mesh with subsequent regression analysis can be utilized to determine necrosis propagation in depth, with a maximum error of only -3.4 % compared to the fine mesh within the considered interval. However, for the necrosis in the lateral direction, the maximum error is 44.3 %, which is too large. Even the mid-size mesh is not accurate enough in the lateral direction, necessitating the use of a fine mesh for the lateral direction.