Finite Volume Method For Hyperbolic Conservation Laws On Manifolds: Convergence Analysis and Error Estimation

The purpose of this book is to lay out a mathematical framework for the convergence and error analysis of the finite volume method for the discretization of hyperbolic conservation laws on manifolds. Finite Volume Method (FVM) is a discretization approach for the numerical simulation of a wide variety physical processes described by conservation law systems. It is extensively employed in fluid mechanics, meteorology, heat and mass transfer, electromagnetic, models of biological processes and many other engineering applications formed by conservative systems. In this book, from one point of view, we provide a brief description for the convergence of the FVM by approaches based on metric and differential forms. The latter can be viewed as a generalization of the formulation and convergence of the method for general conservation laws on curved manifolds. On the other hand, we carried over the error estimate for FVM that is established for the Euclidean setting to the curved manifolds and obtained an expected rate of error in the L1-norm.

Baver Okutmuştur:PhD in Mathematics (2010), Laboratoire Jacques-Louis Lions (LJLL), Université Pierre et Marie Curie (UPMC). Currently Assistant Professor at the Department of Mathematics, Middle East Technical University (METU).