Stability analysis of the nonlinear Galerkin method

Temam, R.

doi:10.1090/S0025-5718-1991-1094959-2

Stability analysis of the nonlinear Galerkin method
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Math. Comp. 57 (1991), 477-505 Request permission

Abstract:

Our object in this article is to describe some numerical schemes for the approximation of nonlinear evolution equations, and to study the stability of the schemes. Spatial discretization can be performed by either spectral or pseudospectral methods, finite elements or finite differences; time discretization is done by two-level schemes, partly or fully explicit. The algorithms that we present stem from the study of the evolution equations from the dynamical systems point of view. They are based on a differentiated treatment of the small and large wave lengths, and they are particularly adapted to the integration of such equations on large intervals of time.

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