Finite Volume Superconvergence Approximation for One-dimesional Singularly Perturbed Problems
نویسندگان
چکیده
We analyze finite volume schemes of arbitrary order r for the one-dimensional singularly perturbed convection-diffusion problem on the Shishkin mesh. We show that the error under the energy norm decays as (Nln(N + 1)), where 2N is the number of subintervals of the primal partition. Furthermore, at the nodal points, the error in function value approximation super-converges with order (Nln(N + 1)), while at the Gauss points, the derivative error super-converges with order (Nln(N + 1)). All the above convergence and superconvergence properties are independent of the perturbation parameter ǫ. Numerical results are presented to support our theoretical findings. Mathematics subject classification: ??
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