Catherine E. Powell's research page



My research is mainly concerned with aspects of numerical analysis related to the numerical solution of partial differential equations (PDEs). In particular, I am interested in the numerical solution of PDE models with uncertain/random inputs, and efficient algorithms for uncertainty quantification (UQ).

Topics: numerical analysis, uncertainty quantification, finite elements, mixed finite elements, error estimation, a posteriori error estimation, adaptivity, stochastic finite elements, numerical linear algebra, saddlepoint systems, fast solvers, iterative solvers, preconditioning.

Current Research Projects


Book

An Introduction to Computational Stochastic PDEs (by G. Lord, C.E. Powell and T. Shardlow). Preface.

This is a textbook designed to introduce recent graduates with a good grounding in applied mathematics and numerical analysis to stochastic differential equations. It assumes no prior knowledge of probability or statistics.

Note that although electronic versions of the book seems to be available from various vendors, the mathematics only displays correctly in pdf format!

MATLAB files associated with the book and solutions (for verified course instructors only) are available HERE .


Software


Journal Papers & Preprints

Most of the following pieces of work can be obtained from journals or as preprints. Copies of older papers which have no active links can be obtained from me by sending me an e-mail and asking nicely.

Theses


Past Research Projects