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- K A Cliffe, A Spence, S J Tavener
- 1999

The steady, axisymmetric laminar flow of a Newtonian fluid past a centrally-located sphere in a pipe first loses stability with increasing flow rate at a steady, O(2)-symmetry breaking bifurcation point. Using group theoretic results, a number of authors have suggested techniques for locating singularities in branches of solutions which are invariant with… (More)

We consider the numerical solution of elliptic partial differential equations with random coefficients. Such problems arise, for example, in uncertainty quantification for groundwater flow. We describe a novel variance reduction technique for the standard Monte Carlo method, called the multilevel Monte Carlo method. The main result is that in certain… (More)

- K A Cliffe, A Spence, S J Tavener
- 2008

In this review we discuss bifurcation theory in a Banach space setting using the singularity theory developed by Golubitsky and Schaeffer to classify bi-furcation points. The numerical analysis of bifurcation problems is discussed and the convergence theory for several important bifurcations is described for both projection and finite difference methods.… (More)

- K A Cliffe, S J Tavener
- 2000

Following the pioneering work of Keller and others in the 1970s and '80s, numerical techniques for solving non-linear systems of equations that exhibit bifurcations have been developed to the point where they can potentially be applied to a wide range of problems arising in continuum mechanics. The central idea is to augment the discre-tised governing… (More)

- S J Tavener, K A Cliffe
- 2002

2 TAVENER Two immiscible fluid layers that are subjected to a temperature gradient perpendicular to their interface, exhibit a range of behaviors that is considerably richer than for the single-fluid case. We describe a numerical technique for calculating thermally-driven flows in two fluid layers which uses a simple technique based on a Landau… (More)

- K A Cliffe, M B Giles, R Scheichl, A L Teckentrup
- 2011

We consider the numerical solution of elliptic partial differential equations with random coefficients. Such problems arise, for example, in uncertainty quantification for groundwater flow. We describe a novel variance reduction technique for the standard Monte Carlo method, called the multilevel Monte Carlo method. The main result is that in certain… (More)

We present the results of a numerical investigation of the Ericksen-Leslie equations for the problem of electrohydrodynamic convection in a nematic liquid crystal. The combination of a finite element approach and numerical bifurcation techniques allows us to provide details of the basic flow and include the physically relevant effect of nonslip side walls.… (More)

- A D Jepson, A Spencer, K A Cliffe
- 1985

The computation of symmetry-breaking bifurcation points of nonlinear multiparameter problems with Z2 (reflectional) symmetry is considered. The numerical approach is based on recent work in singularity theory, which is used to construct systems of equations and inequalities characterising various types of symmetry-breaking bifurcation points. Numerical… (More)

- K A Cliffe, J Collis, P Houston
- 2016

The Nottingham ePrints service makes this work by researchers of the University of Nottingham available open access under the following conditions. · To the extent reasonable and practicable the material made available in Nottingham ePrints has been checked for eligibility before being made available. · Copies of full items can be used for personal research… (More)