Theoretical Optimization of Finite Difference Schemes
  The aim of this work is to develop general optimization methods for finite difference schemes used to approximate linear differential equations. The specific case of the transport equation is exposed. In particular, the minimization of the numerical error is taken into account. The theoretical study of a related linear algebraic problem gives general results which can lead to the determination of the optimal scheme. 
Claire David (LMM), Pierre Sagaut (LMM)