[1][4][5] Silvester was born in Dumfries, but was educated at Ysgol Ardudwy (Wales) and the University of Manchester Institute of Science and Technology (UMIST), from which he gained his B.Sc.
[6] Silvester is best known for his work on finite element methods, fast iterative solvers for fluid dynamics, and uncertainty quantification.
[7] He has more than 65 refereed publications[1] on topics such as iterative solution of Stokes and Navier–Stokes systems, preconditioning, and error estimation in finite element methods.
Silvester's books include Finite Elements and Fast Iterative Solvers: With Applications in Incompressible Fluid Dynamics[7] and Essential Partial Differential Equations (co-authored with David F. Griffiths and John W.
[8] Silvester has served as the elected President of the UK and Republic of Ireland section of the Society for Industrial and Applied Mathematics (2009–2011).