Numerical Studying of PDEs on Manifold with Gaussian Data

The present paper considers PDEs on curves with Gaussian data. We state formulation of elliptic PDE on curves applying recently developed implicit closest point method and drive the cut finite element solution. The Gaussian data is included to the PDE and we drive the required statistics analytically and numerically. Uncertaintyquantification is performed with Monte Carlo sampling method and stochastic Collocation method. Karhunen-Loeve expansion is applied for approximation of random data. The method is numerically implemented to some examples and results illustrating the efficiency of the method.

Numerical Studying of PDEs on Manifold with Gaussian Data Keywords:

Uncertainty Quantification , PDE on curves , Tensor product spaces , Closest point method