Improvement of the Discrete Least Squares Polynomial Approximation for Stochastic Elliptic PDEs via a Reduced Basis Method
In the fields of science and engineering mathematical models are utilized to understand and predict the behavior of complex systems. Common input data/parameters for these type of models include forcing terms, boundary conditions, model coefficients and the computational domain itself. Often times for any number of reasons there is a degree of uncertainty involved with these different types of inputs. In order to obtain an accurate model we must incorporate this uncertainty into the governing equations, and quantify its effects on the output of the simulation. In this work we explore the recently analyzed discrete least squares method and the application of a reduced basis method to cut down on the computational cost.