A graded mesh refinement approach for boundary layer originated singularly perturbed time‐delayed parabolic convection diffusion problems. (30th March 2021)

• Record Type: Journal Article
• Authors: Kumar, Kamalesh; Podila, Pramod Chakravarthy; Das, Pratibhamoy; Ramos, Higinio
• Other Names: Nizovtseva Irina guestEditor.; Alexandrov Dmitri guestEditor.
• Is Part Of: Mathematical methods in the applied sciences. Volume 44:Number 16(2021)
• Page Start: 12332
• Page End: 12350
• Publication Date: 2021-03-30
• Subjects: adaptive mesh algorithm -- algorithmic complexity -- boundary layer phenomena -- entropy -- graded mesh -- parabolic convection–diffusion problems -- time delay; Mathematics -- Periodicals; Technology -- Mathematics -- Periodicals; 519
• DOI: 10.1002/mma.7358
• Languages: English
• ISSNs: 0170-4214

Abstract

Abstract : In this work, we consider a graded mesh refinement algorithm for solving time‐delayed parabolic partial differential equations with a small diffusion parameter. The presence of this parameter leads to boundary layer phenomena. These problems are also known as singularly perturbed problems. For these problems, it is well‐known that one cannot achieve a convergent solution to maintain the boundary layer dynamics, on a fixed number of uniform meshes irrespective of the arbitrary magnitude of perturbation parameter. Here, we consider an adaptive graded mesh generation algorithm, which is based on an entropy function in conjunction with the classical difference schemes, to resolve the layer behavior. The advantage of the present algorithm is that it does not require to have any information about the location of the layer. Several examples are presented to show the high performance of the proposed algorithm.