| Bemerkung |
In this lecture, firstly we will talk about a unified analysis of discontinuous Galerkin methods for elliptic problems. Secondly, we will extend the interior penalty discontinuous Galerkin method to fourth-order elliptic boundary value problems. Thirdly, we will discuss discontinuous Galerkin methods for the linear elasticity problem. In particular, we will prove that the discontinuous Galerkin methods are locking-free and optimal. Fourthly, we will talk about discontinuous Galerkin discretizations for the Stokes problem which preserve the divergence-free condition exactly. Finally, if there is time, we will give an idea on uniformly convergent iterative methods for discontinuous Galerkin discretizations of elliptic problems.
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