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- K. A. Cliffe, T. J. Garratt, Alastair Spence
- Adv. Comput. Math.
- 1993

- K. A. Cliffe, Michael B. Giles, Robert Scheichl, Aretha L. Teckentrup
- Computat. and Visualiz. in Science
- 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)

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)

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
- 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)

Computations of Marangoni convection are usually performed in two-or three-dimensional domains with rigid boundaries. In two dimensions, allowing the free surface to deform can result in a solution set with a qualitatively different bifurca-tion structure. We describe a finite-element technique for calculating bifurcations that arise due to thermal… (More)

- J Steinhelber, V Patterson, K Cliffe, M LeGoullon
- Journal of clinical psychology
- 1984

Psychotherapy supervision has been investigated extensively, but the literature reveals few controlled studies and none that directly assesses the effects of supervision on psychotherapy outcome. In this study, two aspects of psychotherapy supervision--the amount of supervision, and the congruence of theoretical orientation between the supervisor and… (More)

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)

- S J Tavener, T Mullin, G I Blake, K A Cliffe
- Physical review. E, Statistical, nonlinear, and…
- 2001

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)

Unstable concentration gradients inherent in traveling chemical waves can give rise to buoyancy-driven convection, altering the speed of the wave. When an excitable Belousov– Zhabotinsky reaction system is confined within a sufficiently narrow, vertical two-dimensional channel, convection arises at a symmetry-breaking bifurcation point. The observed linear… (More)