C0 — Collocation — Galerkin methods
A C0-Collocation-Galerkin (C0-C-G) method is formulated and analyzed for finite element solution of linear and nonlinear singular boundary-value problems. Theoretical error estimates are ascertained for both the linear problems and a specific class of nonlinear problems. Convergence rates and superconvergence behavior are established and verified in numerical experiments. As a particular class of important research applications, we consider heat and mass transfer problems that arise for catalytic reactors in chemical engineering. The Jacobi points are introduced to determine optimal orders of accuracy and utilized in a new method for determining the boundary flux to optimal order. Numerical results are presented for sample problems.
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- 1.J. Diaz, "A hybrid collocation Galerkin method for the two-point boundary-value problem using continuous piecewise polynomial spaces," Ph.D. thesis, Rice University, Houston, Texas, 1975.Google Scholar
- 2.M.F. Wheeler: "A C0-collocation finite element method for two-point boundary-value problems and one space dimensional parabolic problems," SIAM J. Numer. Anal. Vol. 14, No. 1, 1977.Google Scholar
- 4.M.F. Wheeler and G.F. Carey: "Analysis of collocation-Galerkin methods and Superconvergence for nonlinear two-point problems" (in preparation).Google Scholar
- 5.R.D. Russell and L.F. Shampine: "Numerical methods for singular boundary-value problems," SIAM J. Numer. Anal., Vol. 12, No. 1, 1975.Google Scholar