Ilaria Perugia: [FW] Structure-preserving LDG discretization of nonlinear reaction-diffusion systems

Speaker
Ilaria Perugia, University of Vienna

Abstract
Applications in physics, biology and chemistry often involve PDE systems with multiple interacting components, such as gas mixtures, competing populations, or chemical reactants. These are modeled by nonlinear reaction-diffusion systems. Their numerical approximation is challenging due to nonlinearity, coupling, the need to preserve positivity and boundedness, and often a non-positive definite diffusion matrix. We present numerical methods based on nonlinear transformations involving entropy variables to ensure positivity and boundedness of solutions. We focus on a Local Discontinuous Galerkin (LDG) method, where auxiliary variables help reformulate the problem so that nonlinearities do not appear under differential operators and interface terms. This allows for a parallel evaluation of nonlinear operators, supports high-order accuracy, and provides discrete entropy stability.