Convergence of Orthogonal Collocation on Finite Elements for Parabolic Partial Differential Equations

The convergence behaviour of orthogonal collocation on finite elements is checked for parabolic partial differential equations having mixed and Dirichlet's boundary conditions. The rate of convergence is found to be of the order O(h²). The effect of time gradient on the solution profiles is also checked. It is observed that for small values of the coefficients of , the equation reduces to a singular perturbation problem and the influence of time and space gradients increases. The numerical values approach to steady state condition rapidly for small values of the coefficients of .