Mixed Finite Element Analysis and Numerical Solitary Solution for the RLW Equation

In this paper a mixed finite element (MFE) formulation is proposed for the 1-D regularized long wave (RLW) equation $u_t+auu_x-\delta u_{xxt}=0$. The existence of its mixed generalized solution and semidiscrete and fully discrete mixed finite element solutions is proved, error estimates based on energy methods are given, and finally, results of numerical experiments comparing this formulation with a Galerkin method based on cubic splines are also given.

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