The talk On solving linear systems arising from Shishkin mesh discretizations, by Petr Tichý will be held on Monday April 3, 2017 at 9:00 in room K4.
We consider a convection-diffusion boundary value problem (1D, convection dominated) with Dirichlet boundary conditions. Because of the occurrence of boundary layers in the solution, such problems are difficult to solve numerically. Standard discretization techniques typically cannot resolve the layers and have to be stabilized in order to yield an acceptable numerical solution. Here we consider discretizations using a Shishkin mesh, which clusters mesh points in the layer instead of putting them equidistantly over the whole region, leading to linear algebraic systems with highly nonnormal matrices. In this talk we are interested in solving such systems using the GMRES method and the multiplicative Schwarz method.