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A singularly perturbed parabolic equation of convection-diffusion type with an interior layer in the initial condition is studied. The solution is decomposed into a discontinuous regular component, a continuous outflow boundary layer component and a discontinuous interior layer component. A priori parameter-explicit bounds are derived on the derivatives of these three components. Based on these bounds, a parameter-uniform Shishkin mesh is constructed for this problem. Numerical analysis is presented for the associated numerical method, which concludes by showing that the numerical method is a parameter-uniform numerical method. Numerical results are presented to illustrate the theoretical bounds on the error established in the paper.
}, issn = {2617-8710}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/ijnam/661.html} }A singularly perturbed parabolic equation of convection-diffusion type with an interior layer in the initial condition is studied. The solution is decomposed into a discontinuous regular component, a continuous outflow boundary layer component and a discontinuous interior layer component. A priori parameter-explicit bounds are derived on the derivatives of these three components. Based on these bounds, a parameter-uniform Shishkin mesh is constructed for this problem. Numerical analysis is presented for the associated numerical method, which concludes by showing that the numerical method is a parameter-uniform numerical method. Numerical results are presented to illustrate the theoretical bounds on the error established in the paper.