This paper deals with diffusive limit of the p-system with damping and its approximation by an Asymptotic Preserving (AP) Finite Volume scheme. Provided the system is endowed with an entropy-entropy flux pair, we give the convergence rate of classical solutions of the p-system with damping towards the smooth solutions of the porous media equation using a relative entropy method. Adopting a semi-discrete scheme, we establish that the convergence rate is preserved by the approximated solutions. Several numerical experiments illustrate the relevance of this result.
A numerical comparison between degenerate parabolic and quasilinear hyperbolic models of cell movements under chemotaxis
Istituto per le Applicazioni del Calcolo “Mauro Picone”, Consiglio Nazionale delle Ricerche（意大利国家研究委员会计算应用研究所“毛罗·皮切内”）；Laboratoire J. A. Dieudonné, UMR CNRS 7351, Université de Nice-Sophia Antipolis（尼斯索菲亚安蒂波利斯大学）；Project Team COFFEE, INRIA Sophia Antipolis（INRIA索菲亚安蒂波利斯COFFEE项目组）
Linear, Second order and Unconditionally Energy stable schemes for The Viscous Cahn-Hilliard Equation with hyperbolic relaxation using the invariant energy quadratization method
University of South Carolina（南卡罗来纳大学）；Utah State University（犹他州立大学）
