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arXiv · 2003.06915

Finite-Element Formulation for Advection-Reaction Equations with Change of Variable and Discontinuity Capturing

Stefan Haßler·Anna Maria Ranno·Marek Behr
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Abstract

We propose a change of variable approach and discontinuity capturing methods to ensure physical constraints for advection-reaction equations discretized by the finite element method. This change of variable confines the concentration below an upper bound in a very natural way. For the non-negativity constraint, we propose to use a discontinuity capturing method defined on the reference element that is combined with an anisotropic crosswind-dissipation operator. This discontinuity capturing cannot completely eliminate negative values but effectively minimizes their occurrence. The proposed methods are applied to different biophysical models and show a good agreement with experimental results for the FDA benchmark blood pump for a physiological red blood cell pore formation model.

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Stefan Haßler, Anna Maria Ranno, Marek Behr. 2020-03-15. Finite-Element Formulation for Advection-Reaction Equations with Change of Variable and Discontinuity Capturing. https://doi.org/10.1016/j.cma.2020.113171

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