Durham University Research Reports
Note: The papers listed
here are not all linked to retrievable files
(for historical/copyright reasons).
If you want an offprint, please e-mail the author directly
2005
- Blowey, J.F. and Garvie, M.R. A reaction-diffusion system of $\lambda-\omega$ type Part I: Mathematical analysis European Journal of Applied Mathematics, 15, 1-19.
- Blowey, J.F., Craig, A.W. Frontiers in Numerical Analysis (Durham 2004) Series: Universitext
- Hill, A.A. Double-diffusive convection in a porous medium with a concentration based internal heat source Proc. Roy. Soc. London A, 461, 561 - 574
2004
- Blowey, J.F. and Barrett, J.W. Finite element approximation of a nonlinear cross-diffusion population model Numerische Mathematik, 98, 195---221
- B. Straughan The energy method, stability, and nonlinear convection Vol. 91, Second Edition. Appl. Math. Sci. Ser., Springer-Verlag
- Hill, A.A. Convection induced by the selective absorption of radiation for the Brinkman model Continuum Mechanics and Thermodynamics, 16, 43-52
- Hill, A.A. Conditional and unconditional nonlinear stability for convection induced by absorption of radiation in a porous medium Continuum Mechanics and Thermodynamics, 16, 305-318
- Hill, A.A. Penetrative convection induced by the absorption of radiation with a nonlinear internal heat source Dynamics of Atmospheres and Oceans, 38, 57-67
- J.I. Diaz and B. Straughan Global stability for convection when the viscosity
has a maximum Continuum Mech. Thermodyn., 16, 347--352.
- M. Carr Penetrative convection in a superposed porous-medium-fluid layer via internal heating J. Fluid Mech. 509, 305-329
- Mihai, L.A. & Craig, A.W. A Two-Grid Alternate Strip-Based Domain Decomposition Strategy in Two-Dimensions, Proceedings of Domain Decomposition 15.
- P. Budu Unconditional nonlinear stability in a fluid of 3rd grade. Math. Meth. Appl. Sci. 27, 457-475.
- R. Quintanilla and B. Straughan Discontinuity waves in type III thermoelasticity Proc. Roy. Soc. London A, 460, 1169--1175
2003
- Blowey, J.F., Craig, A.W., Shardlow, T., Frontiers in Numerical Analysis Series: Universitext
- B. Straughan Hydrodynamic stability, the Chebyshev tau method and spurious eigenvalues Continuum Mech. Thermodyn. 15, 571-579
- Coleman, J.P. Order conditions for a class of two-step methods for y''=f(x,y). IMA Journal of Numerical Analysis, Volume 23, 197--220.
- D. Bourne (final year undergraduate project supervised by B.S. Straughan) Hydrodynamic stability, the Chebyshev tau method and spurious eigenvalues Continuum Mech. Thermodyn. 15, 571-579
- F. Franchi and B. Straughan Continuous dependence and decay for the Forchheimer equations Proc. Roy. Soc. London A, 459, 3195--3202
- Hill, A.A. Convection due to the selective absorption of radiation in a porous medium Continuum Mechanics and Thermodynamics, 15, 275 - 285
- M. Carr A model for convection in the evolution of under-ice melt ponds. Continuum Mech. Thermodyn. 15, 45-54.
- M. Carr Unconditional nonlinear stability for temperature dependent density flow in a porous medium. Math. Models Meth. Appl. Sci. 13, 207-22.
- M. Carr and B. Straughan Penetrative convection in a fluid overlying a porous layer Advances in Water Resources, 26, 263--276
- M. Carr and S. de Putter Penetrative convection in a horizontally isotropic layer. Continuum Mech. Thermodyn. 15, 33-43.
2002
- Blowey, J.F. and Barrett, J.W. Finite element approximatin of an Allen-Cahn/Cahn-Hilliard system. IMA Journal of Numerical Analysis, Volume 22, Number 1, pp. 11-71
- B. Straughan Global stability for convection induced by absorption of radiation Dynamics of Atmospheres and Oceans, 35, 351--361
- B. Straughan Effect of property variation and modelling on convection
in a fluid overlying a porous layer. Int. J. Num. Anal. Meth. Geomech. 26, 75-97.
- Coleman, J.P. Order conditions for two-step methods, Submitted to IMA J. Numer. Anal.
- Craig, A.W. and Perella, A.J. A Class of Petrov-Galerkin Methods for the Numerical Solution of the Stationary Convection-Diffusion Equation Submitted to IMAJNA
- Craig, A.W. and Perella, A.J. Numerical Implementation of Locally Adjoint Methods for the Convection-Diffusion Equation Submitted
- Craig, A.W. and Smith, J. Domain decomposition preconditioning for the finite element mass matrix Submitted to Math Comp
- Quintanilla, R. and Straughan, B. Explosive instabilities in heat transmission Proc. Roy. Soc. London A, 458, 2833--2837.
- Straughan, B. Sharp global nonlinear stability for temperature dependent viscosity convection. Proc. Roy. Soc. London A, 458 1773--1782.
2001
- Blowey, J.F. and Barrett, J.W. An Improved Error Bound for a Finite Element Approximation of a Model for Phase Separation of a Multi-Component Alloy with a Concentration Dependent Mobility Matrix Numerische Mathematik 88: 255-297
- Blowey, J.F. and Barrett, J.W. Finite element approximation of a model for order-disorder and phase separationin binary alloys in Numerical Modelling in Continuum Mechanics, Feistauer, M. et al. eds. (Matfyzpress) 1--17
- Blowey, J.F., Coleman, J.P. and Craig, A.W. Theory and Numerics of Differential Equations, Springer
(ISBN: 3-540-41846-6)
- B. Straughan Surface tension driven convection in a fluid overlying
a porous layer. J. Computational Phys. 170 320-337
- B. Straughan Porous Convection, the Chebyshev Tau Method, and Spurious Eigenvalues. In Continuum Mechanics and Applications in Geophysics and the Environment, eds. B. Straughan, R. Greve, H. Ehrentraut and Y. Wang, Springer, pp. 140-152
- Buckwar, E and Shardlow, T Weak approximation of
stochastic delay equations IMA JNA
(Submitted)
- Franchi, F. and Straughan, B. A comparison of the Graffi and Kazhikov-Smagulov models for top heavy pollution instability Advances in Water Resources 24, 585-594
- John W. Barrett, James F. Blowey Finite Element Approximation of a Degenerate Allen--Cahn/Cahn--Hilliard System SIAM Journal on Numerical Analysis, Volume 39, Number 5 pp. 1598-1624
- L.E. Payne, J.F. Rodrigues and B. Straughan Effect of anisotropic permeability on Darcy's Law Math. Meth. Appl. Sci. 24, pp. 427-438
- Paula Budu Stability results for thawing subsea permafrost Continuum Mech Thermodyn 13, 4, 269-285
- Shardlow, T Numerical Methods for Dissipative Particle
Dynamics, SISC
(Submitted)
- Straughan, B. A sharp nonlinear stability threshold in rotating porous convection Proc. Roy. Soc. London A, 457 87--93
2000
- Coleman, J.P. and Duxbury, S.C. Mixed collocation methods for y''=f(x, y), J. Comput. Appl. Math. 126, 47--75
- Payne, L.E. and Straughan, B. A naturally efficient numerical technique for porous convection stability with non-trivial boundary conditions Int. J. Numer. Analytical Methods Geomech., 24, 815-836
- Payne, L.E. and Straughan, B., Unconditional nonlinear stability in temperature - dependent viscosity flow in a porous medium Stud. Appl. Math., 105 , 59-81
- Quintanilla R. and Straughan, B. Growth and uniqueness in thermoelasticity Proc. Roy. Soc. London A, 456 , 1419--1429
- Shardlow,T Stochastic perturbations of the Allen-Cahn equation, 2000 Electron. J. Diff. Eqns., vol. 2000, No. 47, pp. 1-19
- Shardlow, T. and Stuart, A.M. A Perturbation Theory for Ergodic Properties of Markov Chains SIAM J. Num. Anal. vol. 37, no. 4, pp 1120-1137
1999
- Blowey, J.F. and Barrett, J.W. An improved error bound for a finite element approximation of a model for phase separation of a multi-component alloy, IMA Journal of Numerical Analysis 19, pages 147-168.
- Blowey, J.F. and Barrett, J.W. Finite element approximation of a model for phase separation of a multi-component alloy with non-smooth free energy and a concentration dependent mobility matrix, Mathematical Models and Methods in Applied Sciences 9, pages 627-663.
- Blowey, J.F. and Barrett, J.W. Finite element approximation of the Cahn-Hilliard equation with concentration dependent mobility, Mathematics of Computation 68, pages 487-517.
(NA96-02 Durham preprint)
- Blowey, J.F., Barrett, J.W. and Garcke, H. Finite element approximation of the Cahn-Hilliard equation with degenerate mobility, SIAM Journal of Numerical Analysis 37, pages 286-318.
(NA97-07 Durham preprint)
- Payne, L.E. and Straughan, B. Convergence for the equations for a Maxwell fluid Stud. Appl. Math., 103 , 267--278
- Payne, L.E. and Straughan, B. Convergence, continuous dependence and decay for the Brinkman--Forchheimer equations Stud. Appl. Math., 102 , 419--439.
- Payne, L.E. and Straughan, B. Effect of errors in the spatial geometry for temperature dependent Stokes flow J. Math. Pures et Appl., 78 , 609--632.
- Payne, L.E., Song J.C. and Straughan, B. Continuous dependence and convergence results for Brinkman and Forchheimer models with variable viscosity Proc. Roy. Soc. London A, 455 , 2173--2190.
- Shardlow, T. Numerical methods for stochastic parabolic PDEs Numer. Func. Anal. Optim., vol. 20, no. 1-2, pp 121-145
- Shardlow, Tony Geometric Ergodicity of stochastic PDEs Stoch. Anal. App. vol. 17, no 5.
1998
- Blowey, J.F. and Barrett, J.W. Finite element approximation of a model for phase separation of a multi-component alloy with a concentration dependent mobility matrix, IMA Journal of Numerical Analysis, 18, 287-328;
- Blowey, J.F., Barrett, J.W. and Garcke, H. Finite element approximation of a fourth order nonlinear degenerate parabolic equation, Numerische Mathematik 80, 525-556.
(NA97-07 Durham preprint)
- Coleman, J.P. Mixed interpolation methods with arbitrary nodes, J. Compt. Appl. Math. 92, 69-83.
- Payne, L.E. and Straughan, B. Analysis of the boundary condition at the interface between a viscous fluid and a porous medium and related modeling questions J. Math. Pures et Appl., 77 , 317--354
- Payne, L.E. and Straughan, B. Structural stability for the Darcy equations of flow in porous media Proc. Roy. Soc. London A, 454 , 1691--1698.
1997
- A.W. Craig Upwinded restriction operators for nonoverlapping domain decomposition algorithms Domain Decomposition 10, Wiley, 102-111.
- Blowey, J.F. and Barrett, J.W. Finite element approximation of a model for phase separation of a multi-component alloy with non-smooth free energy Numerische Mathematik 77, 1-34.
(NA95-03 Durham preprint)
- K. Hutter and Straughan, B. Penetrative convection in thawing subsea permafrost Continuum Mech. Thermodyn. 9 , 259--272
- Shardlow, T. Inertial Manifolds and Linear Multistep Methods Numerical Algorithms, vol. 14, pp 189-209
- Straughan, B. and D.W. Walker Multi component diffusion and penetrative convection Fluid Dyn. Res. 19 , 77--89
1996
- A.W. Craig Exact Difference Formulae for Linear Differential Operators Numerical Analysis, ed. Griffiths and Watson, World Scientific, 155-163.
- Blowey, J.F. and Barrett, J.W. An Error Bound for the Finite Element Approximation of a Model for Phase Separation of a Multi-Component Alloy IMA Journal of Numerical Analysis 16, 257-287.
- Blowey, J.F., Copetti, M.I.M. and Elliott, C.M. The Numerical Analysis of a Model for Phase Separation of a Multi-Component Alloy IMA Journal of Numerical Analysis 16, 111-139
- Coleman, J.P. and Ixaru, L. Gr. P-stability and exponential-fitting methods for y''=f(x, y) IMA Journal of Numerical Analysis, 16, 179-199.
- Dongarra, J.J., Straughan, B. and Walker, D.W. Chebyshev tau - QZ algorithm methods for calculating spectra of hydrodynamic stability problems Appl. Numer. Math. 22, 399--435
- F. Franchi and Straughan, B Structural stability for the Brinkman equations of porous media Math. Meth. Appl. Sci. 19, 1335--1347
- Mulone, G., Rionero S. and Straughan, B. Unconditional nonlinear stability in a polarized dielectric liquid Atti Accad. Naz. Lincei, (Ser. IX) 7, 241--252.
- Payne, L.E. and Straughan, B. Stability in the initial-time geometry problem for the Brinkman and Darcy equations of flow in porous media J. Math. Pures et Appl., 75, 225--271
- Shardlow, T. Periodic orbits and unstable manifolds Numerical Functional Analysis, vol. 17, no. 9-10, pp 963-989
- Straughan, B. and Walker, D.W. Two very accurate and efficient methods for computing eigenvalues and eigenfunctions in porous convection problems J. Computational Phys. 127, 128--141
- Straughan, B. and Walker, D.W. Anisotropic porous penetrative convection Proc. Roy. Soc. London A, 452, 97--115
1995
1994
1993
- Blowey, J.F. and Elliott, C.M. The Cahn-Hilliard gradient theory for phase separation with non-smooth free energy Part II: Numerical analysis EJAM 3, 147--179
- Coleman, J.P. Numerical methods for y''=f(x, y) In: Proceedings of the First International Colloquium on Numerical Analysis, Plovdiv,Bulgaria, August 1992. (Eds: Bainov, D; Covachev, V) VSP, Utrecht, 27-38
1992
- Blowey, J.F. and Elliott, C.M. Curvature dependent phase boundary motion and parabolic double obstacle problems In: The IMA volumes in mathematics and it applications, vol. 47, Ch. 2, pp. 19-60 (eds. Wei-Ming Ni, L.A. Peletier & J.L. Vazquez), Springer-Verlag
- Coleman, J.P. Rational approximations for the cosine function; P-acceptability and order Numerical Algorithms 3, 143-158
- Coleman, J.P. and Booth, A.S. Analysis of a family of Chebyshev methods for y''=f(x, y) J. Comput. Appl. Math. 44, 95-114