Parameter-uniform approximations for a singularly perturbed\n convection-diffusion problem with a discontinuous initial condition

2020/10/19 by J.L. Gracia, Eugene O’Riordan, Gracia, Jose Luis +1
Engineering · Mathematics · #65M06 #65M12 #65M15 #Differential Equations and Boundary Problems #Differential Equations and Numerical Methods #FOS: Mathematics #Material Science and Thermodynamics #Numerical Analysis (math.NA)

paper · pdf · doi:10.48550/arxiv.2010.09307

openalex publication_date 2020/10/19 · openalex created_date 2022/07/25 · openalex updated_date 2026/07/28

Abstract

A singularly perturbed parabolic problem of convection-diffusion type with a\ndiscontinuous initial condition is examined. A particular complimentary error\nfunction is identified which matches the discontinuity in the initial\ncondition. The difference between this analytical function and the solution of\nthe parabolic problem is approximated numerically. A co-ordinate transformation\nis used so that a layer-adapted mesh can be aligned to the interior layer\npresent in the solution. Numerical analysis is presented for the associated\nnumerical method, which establishes that the numerical method is a\nparameter-uniform numerical method. Numerical results are presented to\nillustrate the pointwise error bounds established in the paper.\n

Related

• Numerical approximations to a singularly perturbed convection-diffusion\n problem with a discontinuous initial condition
• Parameter uniform numerical method for singularly perturbed two parameter parabolic problem with discontinuous convection coefficient and source term
• A parameter uniform method for two-parameter singularly perturbed boundary value problems with discontinuous data
• Singularly perturbed reaction-diffusion problems with discontinuities in the initial and/or the boundary data
• A parameter uniform hybrid approach for singularly perturbed two-parameter parabolic problem with discontinuous data