Invited Lecture
Convergence and error analysis for multidimensional Euler equations
University of Mainz, Germany
Abstract
In this talk I will present our recent results on the convergence analysis of some finite volume and
higher order discontinuous Galerkin methods applied to the Euler equations in two- and three-space
dimensions. In general, we obtain only weak* convergence to a generalized, dissipative measure-valued solution.
If the classical solution exists, the dissipative measure-valued solutions coincide with the classical solution and
the convergence of numerical solutions is strong.
In this case we can also derive the error estimates. To this end we combine the consistency errors
with the continuous form of the relative energy inequality. This allows us to measure an error
between a numerical solution and an exact classical solution. Our approach is general and can
be applied to any consistent numerical method.
The present research has been done in collaboration with Eduard Feireisl, Bangwei She and Philipp Öffner. It has been supported by the Gutenberg Research College and Mainz Institute of Multiscale Modeling.