<p>We study a time-dependent singularly perturbed interior turning point problem. For small perturbation parameter, the solution of the considered problem exhibits twin boundary layers due to the presence of interior turning point. The spatial derivatives are discretized by employing the streamline-diffusion finite element method on a Shishkin-type mesh and an implicit finite difference scheme is applied on uniform mesh for the discretization of temporal derivative. The proposed numerical scheme is stabilized and error estimates are obtained by utilizing an appropriate choice of stabilization parameter and the estimates of discrete Green’s function. The robust convergence results are obtained in both the space and time directions in the maximum norm. The validation of theoretical results is accomplished by taking various numerical examples.</p>

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Error analysis of SDFEM for time-dependent singularly perturbed problem with interior turning point

  • Aasna,
  • Pratima Rai

摘要

We study a time-dependent singularly perturbed interior turning point problem. For small perturbation parameter, the solution of the considered problem exhibits twin boundary layers due to the presence of interior turning point. The spatial derivatives are discretized by employing the streamline-diffusion finite element method on a Shishkin-type mesh and an implicit finite difference scheme is applied on uniform mesh for the discretization of temporal derivative. The proposed numerical scheme is stabilized and error estimates are obtained by utilizing an appropriate choice of stabilization parameter and the estimates of discrete Green’s function. The robust convergence results are obtained in both the space and time directions in the maximum norm. The validation of theoretical results is accomplished by taking various numerical examples.