Finite Volume Multilevel Approximation of the Shallow Water Equations

A priori analysis of multilevel finite volume approximation of 1D convective Cahn–Hilliard equation

“…Next we demonstrate that in all numerical test, the CPU time of the multilevel method is smaller than the one level methods on the fine mesh. Our contribution can be regarded as extension to the works [4,19]. Indeed, in the latter 1D advection equation is analyzed and 2D shallow water linearized around a constant flow is proposed and implemented.…”

“…In this work based on [4], we focus on the solution of the one dimensional CCH equation, with γ = 1, using multilevel finite volume discretization. In many important phenomena (turbulence, excursion, etc ) the solutions involves multi-scale analysis.…”

“…The multilevel method we discus in this paper was formulated by Bousquet and co-workers in [4], in which a hierarchical multilevel finite volume discretization is analyzed. The contribution in [4] is a followup of ideas started in [14,19].…”

“…The multilevel method we discus in this paper was formulated by Bousquet and co-workers in [4], in which a hierarchical multilevel finite volume discretization is analyzed. The contribution in [4] is a followup of ideas started in [14,19]. Our motivation in this work are as follows: formulate, analyze and implement the multilevel approach advocate in [4] for nonlinear partial differential equation with high order derivative.…”

“…The contribution in [4] is a followup of ideas started in [14,19]. Our motivation in this work are as follows: formulate, analyze and implement the multilevel approach advocate in [4] for nonlinear partial differential equation with high order derivative. In [4], the shallow water equations in which the convective term has been linearized around a constant flow is discussed, but here we are interested in a partial differential equation containing the full convective expression uu x and the fact that…”