Least-Squares Proper Generalised Decompositions for Weakly Coercive Elliptic Problems

Proper generalized decompositions (PGDs) are a family of methods for efficiently solving high-dimensional PDEs, which seek to find a low-rank approximation to the solution of the PDE a priori. Convergence of PGD algorithms can only be proven for problems which are continuous, symmetric, and strongly coercive. In the particular case of problems which are only weakly coercive we have the additional issue that weak coercivity estimates are not guaranteed to be inherited by the low-rank PGD approximation. This can cause stability issues when employing a Galerkin PGD approximation of weakly coercive problems. In this paper we propose
The use has been proposed of PGD algorithms based on least-squares formulations which always lead to symmetric and strongly coercive problems and hence provide stable and provably convergent algorithms.

This is the complete data set for the research article "Least-Squares Proper Generalised Decompositions for Weakly Coercive Elliptic Problems” by TLD Croft and TN Phillips, accepted for publication in SIAM Journal on Scientific Computing on 13 April 2017 Volume 39(4), pp. A1366-A1388. (DOI: https://doi.org/10.1137/15M1049269)

It comprises files for the computational models based on least-squares PGDs for weakly coercive problems: Poisson and Stokes.

The source code for the computational model is available on github:

https://github.com/TNPhillips/Least-Squares-PGD