M. Marion and R. Temam, “Nonlinear Galerkin Methods,” SIAM Journal on Numerical Analysis, Vol. 26, No. 5, 1989, pp. 1139-1157. doi:10.1137/0726063
has been cited by the following article:
TITLE: Computational Studies of Reaction-Diffusion Systems by Nonlinear Galerkin Method
AUTHORS: Miroslav Kolář
KEYWORDS: Nonlinear Galerkin Method; Scott-Wang-Showalter Model; Compactness Method
JOURNAL NAME: American Journal of Computational Mathematics, Vol.3 No.2, June 25, 2013
ABSTRACT: This article deals with the computational study of the nonlinear Galerkin method, which is the extension of commonly known Faedo-Galerkin method. The weak formulation of the method is derived and applied to the particular Scott-Wang-Showalter reaction-diffusion model concerning the problem of combustion of hydrocarbon gases. The proof of convergence of the method based on the method of compactness is introduced. Presented results of numerical simulations are composed of the computational study, where the nonlinear Galerkin method and Faedo-Galerkin method are compared for the problem with analytical solution and the numerical results of the Scott-Wang-Showalter model in 1D.