MORE: talk by J. Papež, PhD presentation by A. Janečka and PhD discussion by group B

The talk  A posteriori algebraic error estimation in numerical solution of linear diffusion PDEs, by Jan Papež, will be held on Monday April 7, 2014 at 8:30 in room K4. After that, Adam Janečka will talk about his recent work with a presentation entitled Stability of Flows of Incompressible Implicitly Constituted Fluids Finally, PhD students from group B (Marek Čapek, Martin Michálek, Vit Orava and Josef Žabenský) will do a short progress report of the actual status of their research.

Abstract of the talk

The paper [Ern&Vohralík SISC, 2013], see also the references therein, proposes an adaptive method with a posteriori stopping criteria for numerical solution of nonlinear partial differential equations of diffusion type. The main idea of the method is to distinguish different components of the error, namely the discretization, the linearization, and the algebraic ones, and to design stopping criteria based on balancing these error components. The estimates rely on quasi-equilibrated flux reconstructions and yield a general framework which can be applied to various discretization schemes.

In the present talk we tightly follow [Ern&Vohralík SISC, 2013] and concentrate specifically on estimating the algebraic part of the error. We restrict ourselves to a linear model problem discretized using the conforming finite element method. We show that, with an additional requirement on the flux reconstructions, the algebraic error can be bounded using the algebraic a posteriori error estimator. This justifies the distinction of error components presented in [Ern&Vohralík SISC, 2013]. We show that the flux reconstruction given there can be modified such that the newly introduced requirement is satisfied.

Abstract of the PhD presentation

 We study the stability of steady plane Poiseuille flow of implicitly constituted incompressible fluids. On the channel wall, classical no-slip boundary condition is enforced. The problem is studied within the framework of linearized stability and the resulting generalized Orr-Sommerfeld eigenvalue system of ordinary differential equations is then numerically investigated by means of the spectral collocation methods.