Section: New Results

Numerical schemes

• Very-high order Finite Volume methods: We have showed the very good behavior of a specifically devised domain decomposition technique: the communications are minimized without impacting the accuracy or the order of convergence of the scheme. The total amount of communications dos not increase significantly between the second and the 6th order. The 6th-order Finite-Volume scheme is thus the most performing scheme.

• Numerical analysis of a cartesian method for elliptic problems with immersed interfaces: We have studied the convergence of a cartesian method for elliptic problems with immersed interfaces previously published [54]. The convergence is proved for the original second-order method in one-dimension and for a first-order version in two dimensions. The proof uses a discrete maximum principle to obtain estimates of the coefficients of the inverse matrix.