Singular perturbation with a reduced approximation order in space for the parabolic operator
This work is devoted to singular perturbation of the parabolic equation with discontinuous coefficients for the time operator. For P1 - P0 finite element, by using a reduction of the approximation order for the time differential operator, we propose a numerical method which does not have any oscillations in the neighborhood of the coefficient discontinuity. Error estimates of order tow with respect to space are provided, and we have compared this method with the modified second member method (T.T. Cuc Bui, 2008). Euler explicit and implicit time schemes are proposed, and by considering a toy problem, the order one and tow of convergence with respect to time and space is checked.
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