View abstract

Session I.1 - Multiresolution and Adaptivity in Numerical PDEs

Monday, June 12, 15:30 ~ 16:00

A posteriori error estimates for singularly perturbed equations

Natalia Kopteva

University of Limerick, Ireland   -   This email address is being protected from spambots. You need JavaScript enabled to view it.

Solutions of singularly perturbed partial differential equations typically exhibit sharp boundary and interior layers, as well as corner singularities. To obtain reliable numerical approximations of such solutions in an efficient way, one may want to use meshes that are adapted to solution singularities using a posteriori error estimates. In this talk, we shall discuss residual-type a posteriori error estimates singularly perturbed reaction-diffusion equations and singularly perturbed convection-diffusion equations. The error constants in the considered estimates are independent of the diameters of mesh elements and of the small perturbation parameter. Some earlier results will be briefly reviewed, with the main focus on the recent articles [1, 2] and more recent developments.


[1] N. Kopteva, R. Rankin, Pointwise a posteriori error estimates for discontinuous Galerkin methods for singularly perturbed reaction-diffusion equations, May 2022.

[2] A. Demlow, S. Franz and N. Kopteva, Maximum norm a posteriori error estimates for convection-diffusion problems, IMA J. Numer. Anal., (2023).

Joint work with Alan Demlow (Texas A&M, USA), S. Franz (TU Dresden, Germany) and R. Rankin (University of Nottingham Ningbo, China).

View abstract PDF