Ομιλητής : Natalia Kopteva (U. Limerick, https://staff.ul.ie/natalia/)
Μέρος, ώρα : Παρασκευή 05/05, στις 13:05 στην αίθουσα Σεμιναρίων του Τομέα Μαθηματικών ΣΕΜΦΕ, κτ. Ε΄, 2ος όροφος.
Τίτλος : A posteriori error estimates for singularly perturbed equations.
Περίληψη : “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 reviewed [1], with the main focus on the more recent preprint [2], and a very brief discussion of [3].”
References:
[1] A. Demlow & N. Kopteva, Maximum-norm a posteriori error estimates for singularly perturbed elliptic reaction-diffusion problems, Numer. Math., 133 (2016), 707-742
[2] N. Kopteva, R. Rankin, Pointwise a posteriori error estimates for discontinuous Galerkin methods for singularly perturbed reaction-diffusion equations, preprint, 2022.
[3] A. Demlow, S. Franz and N. Kopteva, Maximum norm a posteriori error estimates for convection-diffusion problems, IMA J. Numer. Anal., (2023), published online 20-Feb-2023.