A singularly perturbed convection-diffusion parabolic problem with incompatible boundary/initial data

Gracia, J.L. (Universidad de Zaragoza) ; O'Riordan, E.

Resumen: A singularly perturbed parabolic problem of convection-diffusion type with incompatible inflow boundary and initial conditions is examined. In the case of constant coefficients, a set of singular functions are identified which match certain incompatibilities in the data and also satisfy the associated homogeneous differential equation. When the convective coefficient only depends on the time variable and the initial/boundary data is discontinuous, then a mixed analytical/numerical approach is taken. In the case of variable coefficients and the zero level of compatibility being satisfied (i.e. continuous boundary/initial data), a numerical method is constructed whose order of convergence is shown to depend on the next level of compatibility being satisfied by the data. Numerical results are presented to support the theoretical error bounds established for both of the approaches examined in the paper.

Idioma: Inglés

DOI: 10.1016/j.apnum.2023.04.011

Año: 2023

Publicado en: APPLIED NUMERICAL MATHEMATICS 190 (2023), 168-186
ISSN: 0168-9274

Financiación: info:eu-repo/grantAgreement/ES/DGA-FSE/E24-17R
Financiación: info:eu-repo/grantAgreement/ES/MICINN PID2019-105979GB-I00

Tipo y forma: Article (Published version)

Área (Departamento): Área Matemática Aplicada (Dpto. Matemática Aplicada)