Conforming Galerkin schemes via traces and applications to plate bending
A talk in the BI.discrete series by
Norbert Heuer
| Abstract: | In recent years the DPG method has raised some attention. It is a
discontinuous Petrov-Galerkin method where the selection of special
test functions guarantees discrete stability. In this way, for a given
well-posed problem, any well-posed variational formulation is
appropriate to set up a Galerkin approximation.
Practical and theoretical reasons suggest to use ultraweak variational
formulations. In this case, field variables are considered in L2 so
that test functions carry all the appearing derivatives. Transferring
derivatives to test functions by integrating by parts, this gives rise
to trace terms and thus, trace operators. In the ultraweak case, trace
operators carry all the regularity weight of the problem. They have to
be defined in appropriate spaces with corresponding images. They also
carry the burden of conformity, when and where wanted.
Independently of the ultraweak formulation and implied DPG scheme, the
conformity of trace approximations is essential to understand and
characterize the conformity of Galerkin schemes in general. We discuss
this relation, and strategies and arising difficulties of this
approach in the case of plate bending models.
Within the CRC this talk is associated to the project(s): A7 |