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Singularly perturbed nonlinear time-dependent parabolic problem with singularly perturbed Neumann boundary conditions

 

A SIM Talk by Catherine Timoney will take place before lunch today Tuesday February 14th Room A2-002

The SIM Talk will consist of a 15 minute presentation followed by discussion.

Speaker: Catherine Timoney, MACSI, Dept. of Mathematics and Statistics, University of Limerick

Topic: Singularly perturbed nonlinear time-dependent parabolic problem with singularly perturbed Neumann boundary conditions

Time: 12.30p.m. Tuesday February 14    Room A2-002

Short Abstract:       This talk will consider work completed during my PhD on finding accurate numerical approximations to nonlinear reaction-diffusion problems that exhibit layer phenomena. It will specifically consider a time-dependent parabolic problem with singularly perturbed Neumann boundary conditions that has boundary and initial layer solutions. In this case the solution in the majority of the domain may not match the boundary or initial conditions and hence areas of rapid change occur in the solution. Numerical examples will be discussed showing the incorrect solutions which can be obtained from solving such a problem in a conventional manner. These incorrect solutions can be cured by adding artificial diffusion to the system which gives correct looking computed solutions. Layer adapted meshes are used to resolve the layer, by giving a fine mesh in the layer region, and to obtain accuracy results in the entire domain. Discrete upper and lower solutions are constructed to prove existence and obtain accuracy results for computed solutions.

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