A discrete Galerkin method for a catalytic combustion model

We apply a novel cost-effective spline method to a one-dimensional model of catalytic combustion in a monolith reactor. The model includes terms for catalytic reaction, heat and mass transfer between the channel wall and the gas, axial conduction in the solid wall, and heat exchange by radiative transfer. This leads to a nonlinear integrodifferential-algebraic system. The computational scheme is based on a discrete Petrov-Galerkin Method, discussed in detail in the recent work [1], and seeks spline approximations to the solutions. It is more cost-effective than the usual orthogonal collocation method and has been proved recently that it retains all stable and optimal convergence properties of the orthogonal collocation on finite elements. It also provides an approach which retains the coupling of the solution components which was not present in previous work on this problem. The numerical experiments obtained using the method are verified against solutions provided in the literature.