Galerkin and collocation‐Galerkin methods with superconvergence and optimal fluxes

Finite element methods are formulated and investigated for the effectiveness factor problem for heat and mass transfer with chemical reactions in catalyst pellet models. A Galerkin finite element method is compared with a previous C1 collocation method7. A scheme that is conceptually intermediate between these two methods and accordingly has been termed collocation-Galerkin is formulated and numerical experiments considered. Of particular interest here are superconvergence results at the Gauss and Jacobi points, respectively. Numerical studies of superconvergence in the presence of a nonlinear reaction-rate term are presented. An integral formula is devised and used to compute the flux at the pellet surface to optimal accuracy. Numerical experiments are conducted to demonstrate the improvement in computed fluxes.

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