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bioRxiv · 10.1101/2025.10.27.684936

A FINITE ELEMENT FRAMEWORK FOR BULK-SURFACE COUPLED PDES TO SOLVE MOVING BOUNDARY PROBLEMS IN BIOPHYSICS

Contri, A.·Massing, A.·Rangamani, P.
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Abstract

We consider moving boundary problems for biophysics and introduce a new computational framework to handle the complexity of the bulk-surface PDEs. In our framework, interpretability is maintained by adapting the fast, generalizable and accurate structure preservation scheme in [29]. We show that mesh distortion is mitigated by adopting the pioneering work of [36], which is tied to an Arbitrary Lagrangian Eulerian (ALE) framework. We test our algorithms accuracy on moving surfaces with boundary for the following PDEs: advection-diffusion-reaction equations, phase-field models of Cahn-Hilliard type, and Helfrich energy gradient flows. We performed convergence studies for all the schemes introduced to demonstrate accuracy. We use a staggered approach to achieve coupling and further verify the convergence of this coupling using numerical experiments. Finally, we demonstrate broad applicability of our work by simulating state-of-the-art tests of biophysical models that involve membrane deformation.

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Contri, A., Massing, A., Rangamani, P.. 2025-10-28. A FINITE ELEMENT FRAMEWORK FOR BULK-SURFACE COUPLED PDES TO SOLVE MOVING BOUNDARY PROBLEMS IN BIOPHYSICS. https://doi.org/10.1101/2025.10.27.684936

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