Sharp a priori fully discrete finite element error estimates for parabolic problems

Prof. Dr. Dimitriy Leykekhman (University of Connecticut, USA)

Abstract

The aim of this minicourse is to present a recent development in the area of fully discrete Galerkin approximations of parabolic equations with emphasis on a priori error estimates. In this course I will review the classical results and present a new technique based on discrete maximatial parabolic regularity that allow us to establish best approximation properties of the discrete solutions in L∞ norm in two and three space dimensions. The lectures will roughly consists of the following topics:

• Review of the classic theory of the error estimates in energy type norms.

• Finite element space discretization. Elliptic theory

• Resolvent and weighted resolvent estimates.

• Discontinuous Galerkin time discretization.

• Discrete discrete maximum regularity.

• Global and interior pointwise error estimates.

The main body of the course is based on a series of papers with Prof. Boris Vexler that have appeared in the last two years.

Registration

No registration required.

Date and Place

• Thursday, 20.07.17:
  • 10:30 - 12:00 and 13:00 - 14:30 in LRZ, Seminarroom 1 on ground floor.

• Friday, 21.07.17:
  • 10:30 - 12:00 in 02.10.011
  • 14:15 - 15:45 in 02.04.011

• Monday, 24.07.17:
  • 10:30 - 12:00 in 03.04.011
  • 14:15 - 15:45 in 03.06.011

• Tuesday 25.07.17:
  • 10:30 - 12:00 in 02.04.011
  • 14:15 - 15:45 in 03.08.011

-- DianeClaytonWinter - 24 Feb 2017