Finite element approximation of the very weak formulation of singular-degenerate SPDEs
A talk in the BI.discrete Workshop series by
L’ubomír Baňas from Bielefeld
| Abstract: | The very weak formulation is useful to give meaning to solutions of singular-degenerate stochastic partial differential equations (SPDEs)
in the low regularity setting, e.g., when the considered noise is the space-time white noise.
We consider a fully discrete numerical scheme for the approximation of singular-degenerate SPDEs in the very weak formulation.
Using the monotonicity properties of the very weak formulation we show that the proposed numerical scheme converges to the (probabilistically) strong solutions of the considered SPDEs.
We present a non-standard finite element based spatial approximation of the problem which yields an efficient numerical algorithm in higher spatial dimensions.
We also show how the very weak approach can be applied to standard finite element discretization schemes by exploiting their connection to the finite-difference schemes.
Finally, we demonstrate the need for the very weak formulation by numerical experiments for model problems with space-time white noise.
The talk is based on joint work with Benjamin Gess, Marius Neuss and Christian Vieth. Within the CRC this talk is associated to the project(s): B7 |