Professor John Whiteman

Contact

Mathematical Sciences John Crank 305 Brunel University Uxbridge UB8 3PH United Kingdom

Tel: +44 (0)1895 265185 Email: john.whiteman@brunel.ac.uk

Research Interests

Numerical methods for partial differential equations, particularly in the context of solid mechanics. Finite element methods for problems of linear elasticity, elastoplasticity and viscoelasticity; gradient recovery and superconvergence. Treatment of fracture problems, particularly viscoelastic fracture. Industrial applications of continuum mechanics problems.

University Research Centre Membership

Publications

Journal Papers

(2010) Shaw, S., Warby, MK. and Whiteman, JR., Discretization error and modelling error in the context of the rapid inflation of hyperelastic membranes, IMA Journal of Numerical Analysis 30 (1) : 302- 333 Download publication

(2007) Rivière, B., Shaw, S. and Whiteman, JR., Discontinuous Galerkin finite element methods for dynamic linear solid viscoelasticity problems, Numerical Methods for Partial Differential Equations 23 (5) : 1149- 1166

(2006) Karamanou, M., Warby, MK. and Whiteman, JR., Computational modelling of thermoforming processes in the case of finite viscoelastic materials, Computer Methods in Applied Mechanics and Engineering 195 (37-40) : 5220- 5238

(2005) Karamanou, M., Shaw, S., Warby, MK. and Whiteman, JR., Models, algorithms and error estimation for computational viscoelasticity, Computer Methods in Applied Mechanics and Engineering 194 (2-5) : 245- 265

(2004) Shaw, S. and Whiteman, JR., A posteriori error estimates for space–time finite element approximation of quasistatic hereditary linear viscoelasticity problems, Computer Methods in Applied Mechanics and Engineering 193 (52) : 5551- 5572

(2004) Kuczma, MS., Litewka, P., Rakowski, J. and Whiteman, JR., A variational inequality approach to an elastoplastic plate-foundation system, Foundations of Civil and Environmental Engineering 4 31- 48

(2003) Rivière, B., Shaw, S., Wheeler, MF. and Whiteman, JR., Discontinuous Galerkin finite element methods for linear elasticity and quasistatic linear viscoelasticity, Numerische Mathematik 95 (2) : 347- 376

(2003) Ludwig, MJ., Shaw, S. and Whiteman, JR., Adaptive numerical solution of thick plates using first-order shear deformation theory. Part 1: error estimates, Numerical Methods for Partial Differential Equations 19 (1) : 44- 66

(2003) Ludwig, MJ., Shaw, S. and Whiteman, JR., Adaptive numerical solution of thick plates using first-order shear deformation theory. Part II: adaptivity, Numerical Methods for Partial Differential Equations 19 (2) : 227- 253

(2003) Jiang, W-G., Warby, MK., Whiteman, JR., Abbott, S., Shorter, W., Warwick, P., Wright, T., Munro, A. and Munro, B., Finite element modelling of high air pressure forming processes for polymer sheets, Computational Mechanics 31 (1-2) : 163- 172

(2003) Warby, MK., Whiteman, JR., Jiang, W-G., Warwick, P. and Wright, T., Finite element simulation of thermoforming processes for polymer sheets, Mathematics and Computers in Simulation 61 (3-6) : 209- 218

(2001) Shaw, S. and Whiteman, JR., Optimal long-time Lp(0, T) stability and semidiscrete error estimates for the Volterra formulation of the linear quasistatic viscoelasticity problem, Numerische Mathematik 88 (4) : 743- 770

(2001) Kirby, JA., Warby, MK. and Whiteman, JR., Superconvergence and an error estimator for the finite element analysis of beams and frames, Numerical Methods for Partial Differential Equations 17 (2) : 169- 197

(2000) Shaw, S. and Whiteman, JR., Adaptive space-time finite element solution for Volterra equations arising in viscoelasticity problems, Journal of Computational and Applied Mathematics 125 (1-2) : 337- 345

(2000) Andrä, H., Warby, MK. and Whiteman, JR., Contact problems of hyperelastic membranes: existence theory, Mathematical Methods in the Applied Sciences 23 (10) : 865- 895

(2000) Shaw, S. and Whiteman, JR., Negative norm error control for second-kind convolution Volterra equations, Numerische Mathematik 85 (2) : 329- 341

(2000) Shaw, S. and Whiteman, JR., Numerical solution of linear quasistatic hereditary viscoelasticity problems, SIAM Journal on Numerical Analysis 38 (1) : 80- 97

(2000) Rohan, E. and Whiteman, JR., Shape optimization of elasto-plastic structures and continua, Computer Methods in Applied Mechanics and Engineering 187 (1-2) : 261- 288

(2000) Lakhany, AM., Marek, I. and Whiteman, JR., Superconvergence results on mildly structured triangulations, Computer Methods in Applied Mechanics and Engineering 189 (1) : 1- 75

(1997) Shaw, S., Warby, MK. and Whiteman, JR., Error estimates with sharp constants for a fading memory Volterra problem in linear solid viscoelasticity, SIAM Journal on Numerical Analysis 34 (3) : 1237- 1254

(1997) Hlaváček, I. and Whiteman, JR., Existence and uniqueness of solutions in strain space of elastoplastic problems with isotropic hardening, Mathematical Models and Methods in Applied Sciences 7 (1) : 31- 48

(1996) Shaw, S. and Whiteman, JR., Discontinuous Galerkin method with a posteriori L_p(0,t(i)) error estimate for second-kind Volterra problems, Numerische Mathematik 74 (3) : 361- 383

(1996) Shaw, S., Warby, MK. and Whiteman, JR., Discrete schemes for treating hereditary problems of viscoelasticity and applications, Journal of Computational and Applied Mathematics 74 (1-2) : 313- 329

(1996) Apel, T., Sändig, A-M. and Whiteman, JR., Graded mesh refinement and error estimates for finite element solutions of elliptic boundary value problems in non-smooth domains, Mathematical Methods in the Applied Sciences 19 (1) : 63- 85

(1996) Shaw, S. and Whiteman, JR., Towards adaptive finite element schemes for partial differential Volterra equation solvers, Advances in Computational Mathematics 6 (1) : 309- 323

(1995) Mücke, R. and Whiteman, JR., A posteriori error estimates and adaptivity for finite element solutions in finite elasticity, International Journal for Numerical Methods in Engineering 38 (5) : 775- 795

(1995) Janovsky, V., Shaw, S., Warby, MK. and Whiteman, JR., Numerical methods for treating problems of viscoelastic isotropic solid deformation, Journal of Computational and Applied Mathematics 63 (1-3) : 91- 107

(1995) Kuczma, MS. and Whiteman, JR., Variational inequality formulation for flow theory plasticity, International Journal of Engineering Science 33 (8) : 1153- 1169

(1994) Shaw, S., Warby, MK., Whiteman, JR., Dawson, C. and Wheeler, MF., Numerical techniques for the treatment of quasistatic viscoelastic stress problems in linear isotropic solids, Computer Methods in Applied Mechanics and Engineering 118 (3-4) : 211- 237

(1992) Warby, MK., Walton, JR. and Whiteman, JR., A finite element model of crack growth in a finite body in the context of mode I linear viscoelastic fracture, Computer Methods in Applied Mechanics and Engineering 97 (3) : 375- 397

(1992) Darwish, MS., Whiteman, JR. and Bevis, MJ., Numerical modelling of viscoelastic liquids using a finite-volume method, Journal of Non-Newtonian Fluid Mechanics 45 (3) : 311- 337

(1992) Hlaváček, I., Rosenberg, J., Beagles, AE. and Whiteman, JR., Variational inequality formulation in strain space and finite element solution of an elasto-plastic problem with hardening, Computer Methods in Applied Mechanics and Engineering 94 (1) : 93- 112

(1989) Goodsell, G. and Whiteman, JR., A unified treatment of superconvergent recovered gradient functions for piecewise linear finite element approximations, International Journal for Numerical Methods in Engineering 27 (3) : 469- 481

(1989) Beagles, AE., Whiteman, JR. and Wendland, W., General conical singularities in three-dimensional Poisson problems, Mathematical Methods in the Applied Sciences 11 (2) : 215- 235

(1988) Aston, PJ. and Whiteman, JR., Analysis of two-way snap of shells of revolution, International Journal of Engineering Science 26 (7) : 687- 702

(1988) Warby, MK. and Whiteman, JR., Finite element model of viscoelastic membrane deformation, Computer Methods in Applied Mechanics and Engineering 68 (1) : 33- 54

(1988) Stephan, E. and Whiteman, JR., Singularities of the Laplacian at corners and edges of three-dimensional domains and their treatment with finite element methods, Mathematical Methods in the Applied Sciences 10 (3) : 339- 350

(1984) Yettram, AL., Whiteman, JR. and Henwood, DJ., Effect of thickness on the behaviour of plates on foundations, Computers and Structures 19 (4) : 501- 509

(1982) Oden, JT. and Whiteman, JR., Analysis of some finite element methods for a class of problems in elasto-plasticity, International Journal of Engineering Science 20 (9) : 977- 988

(1982) Harrison, D., Ward, TJW. and Whiteman, JR., Finite element analysis of plates with nonlinear properties, Computer Methods in Applied Mechanics and Engineering 34 (1-3) : 1019- 1034

(1982) Henwood, DJ., Whiteman, JR. and Yettram, AL., Fourier series solution for a rectangular thick plate with free edges on an elastic foundation, International Journal for Numerical Methods in Engineering 18 (12) : 1801- 1820

(1981) Henwood, DJ., Whiteman, JR. and Yettram, AL., Finite difference solution of a system of first-order partial differential equations, International Journal for Numerical Methods in Engineering 17 (9) : 1385- 1395

(1979) Janovsky, V. and Whiteman, JR., Error analysis of finite element methods for mildly nonlinear variational inequalities, Numerical Functional Analysis and Optimization 1 (3) : 223- 232

(1978) Gregory, JA., Fishelov, D., Schiff, B. and Whiteman, JR., Local mesh refinement with finite elements for elliptic problems, Journal of Computational Physics 29 (1) : 133- 140

(1976) Noor, MA. and Whiteman, JR., Error bounds for finite element solutions of mildly nonlinear elliptic boundary value problems, Numerische Mathematik 26 (1) : 107- 116

(1975) Barnhill, RE. and Whiteman, JR., Error analysis of Galerkin methods for Dirichlet problems containing boundary singularities, IMA Journal of Applied Mathematics 15 (1) : 121- 125

(1973) Papamichael, N. and Whiteman, JR., A numerical conformal transformation method for harmonic mixed boundary value problems in polygonal domains, Zeitschrift für Angewandte Mathematik und Physik (ZAMP) 24 (3) : 304- 316

(1972) Whiteman, JR. and Papamichael, N., Treatment of harmonic mixed boundary problems by conformal transformation methods, Zeitschrift für Angewandte Mathematik und Physik (ZAMP) 23 (4) : 655- 664

Conference Papers

(2003) Karamanou, M., Shaw, S., Warby, MK. and Whiteman, JR., Models, algorithms and error estimation for computational viscoelasticity, 11th Conference on Mathematics of Finite Elements and Applications (MAFELAP 2003)

(2007) Szegda, D., Song, J., Warby, MK. and Whiteman, JR., Computational modelling of a thermoforming process for thermoplastic starch, AIP Conference Proceedings: Materials Processing and Design; Modelling, Simulation and Applications, 908 35- 48

(2003) Warby, MK., Whiteman, JR., Jiang, W-G., Warwick, P. and Wright, T., Finite element simulation of thermoforming processes for polymer sheets, 2nd IMACS Conference on Mathematical Modelling and Computational Methods in Mechanics, Physics, Biomechanics and Geodynamics, Mathematics and Computers in Simulation (61) : 209- 218

(2000) Shaw, S., Johnson, AR. and Whiteman, JR., Modelling and finite element analysis of applied polymer viscoelasticity problems, 10th Conference on the Mathematics of Finite Elements and Applications (MAFELAP 1999)

(1997) Shaw, S. and Whiteman, JR., Applications and numerical analysis of partial differential Volterra equations: a brief survey, Interdisciplinary Symposium on Advances in Computational Mechanics in Honor of Professor John Tinsley Oden, Computer Methods in Applied Mechanics and Engineering (150) : 397- 409

Book Chapters

(1998) Lakhany, AM. and Whiteman, JR., Superconvergent recovery operators: derivative recovery techniques. In: Krizek, M., Neittaanmaki, P. and Stenberg, R. eds. Finite Element Methods. (196) : 195- 215

(1989) Whiteman, JR. and Goodsell, G., Some gradient superconvergence results in the finite element method. In: Turner, P. ed. Numerical Analysis and Parallel Processing. (1397/1989) : 182- 260

(1986) Whiteman, JR., Singularities in two- and three-dimensional elliptic problems and finite element methods for their treatment. In: Vosmansky, J. and Zlamal, M. eds. Equadiff 6. (1192/1986) : 345- 352

(1984) Whiteman, JR., Singularities in three-dimensional elliptic problems and their treatment with finite element methods. In: Griffiths, DF. ed. Numerical Analysis. (1066/1984) : 264- 275

(1985) Beagles, AE. and Whiteman, JR., Treatment of a re-entrant vertex in a three-dimensional poisson problem. In: Grisvard, P., Wendland, W. and Whiteman, JR. eds. Singularities and Constructive Methods for Their Treatment. (1121/1985) : 19- 27