Local defect correction techniques: analysis and application to combustion (Q2760878)

This is an excellent PhD thesis. In the introduction the author first gives the background and an outline of the thesis, where he comments on the problems attacked in the subsequent chapters. Besides, he comments on the models that he studies in the thesis as well as the methods that will be used. In Chapter II, the author studies a mathematical model for a stationary laminar flame. Chapter III describes the two-grid local defect correction method, giving examples and some important properties, and gives the formulation of the LDC method, that will be used in Chapter IV where he studies an LDC method for finite volume discretizations. In this Chapter he also describes in a complete way the formulation of the problem and finite volume discretization on the uniform grid and an iterative finite volume discretization on composite grids. Besides this chapter concludes with some numerical experiments. 1. The two-dimensional interface problem and 2. The one-dimensional convection-diffusion problem. NEWLINENEWLINENEWLINEThe study of the convergence behaviour of the LDC method as an iterative process is done by the author in Chapter V. In Chapter VI he studies adaptive multi-level in combination with domain decomposition. Finally, numerical simulation of the Bunsen flame has been studied in the Chapter VII. Here he studies in a substantial way discretization of partial differential equations, solving the discrete system and finally the author gives several numerical results. In the final Chapter VIII, he gives conclusions and recommendations of the results obtained.