Gabriel R. Barrenechea – författare

This volume gathers papers presented at the international conference BAIL, which was held at the University of Strathclyde, Scotland from the 14th to the 22nd of June 2018. The conference gathered specialists in the asymptotic and numerical analysis of problems which exhibit layers and interfaces. Covering a wide range of topics and sharing a wealth of insights, the papers in this volume provide an overview of the latest research into the theory and numerical approximation of problems involving boundary and interior layers.

This book offers a comprehensive presentation of numerical methods for elliptic boundary value problems that satisfy discrete maximum principles (DMPs). The satisfaction of DMPs ensures that numerical solutions possess physically admissible values, which is of utmost importance in numerous applications. A general framework for the proofs of monotonicity and discrete maximum principles is developed for both linear and nonlinear discretizations. Starting with the Poisson problem, the focus is on convection-diffusion-reaction problems with dominant convection, a situation which leads to a numerical problem with multi-scale character. The emphasis of this book is on finite element methods, where classical (usually linear) and modern nonlinear discretizations are presented in a unified way. In addition, popular finite difference and finite volume methods are discussed. Besides DMPs, other important properties of the methods, like convergence, are studied. Proofs are presented step by step, allowing readers to understand the analytic techniques more easily. Numerical examples illustrate the behavior of the methods.