CONTENTS

How to request a hardcopy of the Departmental Brochure

The Numerical Analysis Group

Research Interests within the Group

Recent Publications

Links:

• About this page.
• Postgraduate study in the Department
• Durham Numerical Analysis home page
• Department of Mathematical Sciences home page.
• The University of Durham home page

Numerical Analysis Group

There are three members of staff in the numerical analysis group:

James F Blowey

phase transitions and finite element analysis

Alan W Craig

finite element and multigrid methods

Brian Straughan

Flow in porous media, Thermal convection, Spectral methods.

In the last national research assessment by HEFCE, applied mathematics, which includes our group, was awarded a 5^*, the highest grade.

Research Interests

The interests of the group range over a wide variety of topics within the field of numerical analysis. These include:

• Faber polynomials, and polynomial and rational approximations of complex-valued functions, see [1], [2].
• Numerical methods for ordinary differential equations, see [3], [4].
• Numerical solution of partial differential equations: Finite element, Finite volume and multigrid methods, see [5], [6], [7].
• Analytical and numerical study of phase transitions, see [8], [9], [10].

There is a weekly seminar in term time. We have a World Wide Web page where you will find up to date information about seminars, publications and research interests.

Recent Publications

[1]

J.P. Coleman, Rational approximations for the cosine function; P-acceptability and order, Numer. Algorithms 3, 143-158 (1992).

[2]

J.P. Coleman & N.J. Myers, The Faber polynomials for annular sectors, Math. Comp. 64, 181-203 (1995).

[3]

J.P. Coleman & L.Gr. Ixaru, P-stability and exponential-fitting methods for y''=f(x,y), IMA Journal of Numerical Analysis, 16, pp. 179-199 (1996).

[4]

J.P. Coleman & A.S. Booth, The Chebyshev methods of Panovsky and Richardson as Runge-Kutta-Nystrom methods, J. Comput. Appl. Math. 61, pp. 245-261 (1995).

[5]

J.W. Barrett & J.F. Blowey, An Error Bound for the Finite Element Approximation of the Cahn-Hilliard Equation with Logarithmic Free Energy, Numerische Mathematik, 72, pp. 1-20 (1995).

[6]

M. Ainsworth & A.W. Craig, A posteriori error estimation in the finite element method, Numer. Math. 60, 429-463 (1992).

[7]

I. Babuska, A.W. Craig, J. Mandel and J. Pitkaranta, Efficient preconditioning for the p-version of the finite element method in two dimensions, SIAM J. Num. Anal. 28 (1991).

[8]

J.F. Blowey, M.I.M. Copetti & C.M. Elliott, The numerical analysis of a model for phase separation of a multi-component alloy, IMA Journal of Numerical Analysis, 16, pp. 111-139 (1996).

[9]

J.F. Blowey & C.M. Elliott, A phase field model with double obstacle potential, In: MOTION BY MEAN CURVATURE AND RELATED TOPICS, (Eds. Buttazzo,G; Visintin,A), de Gruyter pp.1-22 (1994).

[10]

J.F. Blowey & C.M. Elliott, Curvature dependent phase boundary motion and parabolic double obstacle problems, In: THE IMA VOLUMES IN MATHEMATICS AND ITS APPLICATIONS, vol. 47, (Eds. Wei-Ming, Ni; Peletier,L.A.; Vazquez,J.L.), Springer-Verlag pp.19-60 (1993).

More recent research reports and publications are available electronically.

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Revised 22/5/97.