Parameter-Robust Discretizations and Solvers for Singularly Perturbed PDEs (Scott MacLachlan, Tufts University)
Mittwoch 18.10.2017, 10 Uhr, Raum G.15.20
In order to resolve important features of solutions to singularly perturbed differential equations, specialized discretization techniques are needed. Layer-adapted meshes allow "parameter-robust” discretizations, which offer accuracy bounded independently of the perturbation parameter, and provide significant structure to the resulting linear systems. In this talk, I will present recent results on parameter-robust finite-element discretizations, building on the framework of "balanced norms". I will also discuss tuned preconditioners for finite-difference and finite-element discretizations on layer-adapted meshes, offering robustness to variations in both mesh size and perturbation parameter. This is joint work with Niall Madden and Thai Anh Nhan from the National University of Ireland, Galway, and James Adler from Tufts University.
