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A. R. MITCHELL: PUBLICATIONS

 

BOOKS

  1. Computational Methods in Partial Differential Equations. J. Wiley & Sons, London, 1969.
  2. Finite Element Methods in Partial Differential Equations. J. Wiley & Sons, London, 1976. (with R. Wait).
  3. The Finite Difference Method in Partial Differential Equations. J. Wiley & Sons, London, 1980. (with D. F. Griffiths).
  4. Finite Element Analysis and Applications. J. Wiley & Sons, London, 1985. (with R. Wait).

PAPERS

  1. Application of relaxation methods to compressible flow past a double wedge. Proc. Roy. Soc. Edinburgh, 63:139-154, 1951. (with D. E. Rutherford).
  2. Application of relaxation to the rotational flow behind a bow shock wave. Quart. J. Mech. and Appl. Math., 4:371-383, 1951.
  3. The rotational field behind a bow shock wave in axially symmetric flow using relaxation methods. Proc. Roy. Soc. Edinburgh, 63:371-380, 1952.
  4. Stability of difference relations in the solution of ordinary differential equations. Math. Tables and other Aids to Comp., 7:127-129, 1953. (with J. W. Craggs).
  5. Round-off errors in the solution of the heat conduction equation by relaxation methods. Appl. Sci. Res., 3:109-119, 1953.
  6. Round-off errors in relaxation solutions of Poisson's equation. Appl. Sci. Res., 4:456-454, 1954.
  7. On the theory of relaxation. Proc. Glasgow Math. Assoc., 1:101-110, 1955. (with D. Rutherford).
  8. Two dimensional flow with constant shear past cylinders with various cross sections. ZAMP, 6:223-235, 1957. (with J. D. Murray).
  9. Round-off errors in implicit finite difference methods. Quart. J. Mech. and Appl. Math., 9:111-121, 1956.
  10. Flow with variable shear past circular cylinders. Quart. J. Mech. and Appl. Math., 10:13-23, 1957. (with J. D. Murray).
  11. Boundary value techniques for initial value problems in ordinary differential equations. Quart. J. Mech. and Appl. Math., 10:232-243, 1957. (with L. Fox).
  12. The application of finite difference methods to the solution of problems in boundary layer flow. Proc. Int. Appl. Math. Congress, Brussels, 1957. (with J. Y. Thompson).
  13. Finite difference methods of solution of the Von Mises boundary layer equation with special reference to conditions near a singularity. ZAMP, 9:26-37, 1958. (with J. Y. Thompson).
  14. The influence of critical boundary conditions on finite difference solutions of two point boundary problems. Math. Tables and other Aids to Comp., 13:252-260, 1959.
  15. The effect of boundary condition and mesh size on the accuracy of finite difference solutions of two point boundary value problems. ZAMP, 10:221-232, 1959. (with D. Borwein).
  16. Solution of the Von Mises boundary layer equation using a high speed computer. Math. Comp., 15:238-242, 1961.
  17. On the solution of y' = f(x,y) by a class of high accuracy difference formulae. ZAMP, 13:223-232, 1962. (with J. D. Lambert).
  18. On finite difference methods of solution of the transport equation. Math. Comp., 16:155-169, 1962. (with R. P. Pearce).
  19. High accuracy difference formulae for the numerical solution of the heat conduction equation. The Computer Journal, 5:142-146, 1963. (with R. P. Pearce).
  20. The use of higher derivatives in quadrature formulae. The Computer Journal, 5:322-327, 1963. (with J. D. Lambert).
  21. Repeated quadrature using derivatives of the integrand. ZAMP, 15:84-90, 1964. (with J. D. Lambert).
  22. Explicit difference methods for solving the cylindrical heat conduction equation. Math. Comp., 17:426-432, 1963. (with R. P. Pearce).
  23. A generalised ADI method of Douglas-Rachford type for solving the biharmonic equation. The Computer Journal, 7:242-245, 1964. (with G. Fairweather).
  24. Improved forms of the ADI methods of Douglas, Peaceman and Rachford for solving parabolic and elliptic equations. Numer. Math., 6:285-292, 1964. (with G. Fairweather).
  25. A new ADI method for parabolic equations in three space variables. SIAM J., 13:957-965, 1965. (with G. Fairweather).
  26. A high accuracy ADI method for the wave equation. J. Inst. Maths Applics., 1:309-316, 1965. (with G. Fairweather).
  27. Some computational results of an improved ADI method for the Dirichlet problem. The Computer Journal, 9:9-15, 1966. (with G. Fairweather).
  28. Two level difference schemes for hyperbolic systems. SIAM J. Numer. Anal., 3:474-485, 1966. (with A. R. Gourlay).
  29. A stable implicit difference method for hyperbolic systems in two space variables. Numer. Math., 8:367-375, 1966. (with A. R. Gourlay).
  30. Alternating direction methods for hyperbolic systems. Numer. Math., 8:137-149, 1966. (with A. R. Gourlay).
  31. On the instability of the Crank-Nicholson formula under derivative boundary conditions. The Computer Journal, 9:110-114, 1966. (with P. Keast).
  32. Split operator methods for hyperbolic systems in p space variables. Math. Comp., 21:351-354, 1967. (with A. R. Gourlay).
  33. Intermediate boundary corrections for split operator methods in three dimensions. BIT, 7:31-38, 1967. (with A. R. Gourlay).
  34. Finite difference solution of the third boundary problem in elliptic and parabolic equations. Numer. Math., 10:67-75, 1967. (with P. Keast).
  35. A new computational procedure for ADI methods. SIAM J. Numer. Anal., 4:163-170, 1967. (with G. Fairweather).
  36. Some high accuracy difference schemes with a splitting operator for equations of parabolic and elliptic type. Numer. Math., 10:56-66, 1967. (with G. Fairweather and A. R. Gourlay).
  37. High accuracy ADI methods for parabolic equations with variable coefficients. Numer. Math., 12:180-185, 1968. (with A. R. Gourlay).
  38. The equivalence of certain alternating direction and locally one-dimensional difference methods. SIAM J. Numer. Anal., 6:37-46, 1969. (with A. R. Gourlay).
  39. A classification of split difference methods for hyperbolic equations in several space dimensions. SIAM J. Numer. Anal., 6:62-71, 1969. (with A. R. Gourlay).
  40. Alternating direction methods for parabolic equations in two space dimensions with a mixed derivative. The Computer Journal, 13:81-86, 1970. (with S. McKee).
  41. Splitting methods in partial differential equations. Abhandlungen aus dem Mathematischen Seminar der Universität Hamburg, 36:45-56, 1971.
  42. The solution of time dependent problems by Galerkin methods. J. Inst. Maths Applics., 7:241-250, 1971. (with R. Wait).
  43. The finite element method in partial differential equations. Methoden und Verfahren der Mathematischen Physik, 5:101-115, 1971.
  44. Corner singularities in elliptic problems by finite element methods. J. Comp. Phys., 8:45-52, 1971. (with R. Wait).
  45. Alternating direction methods for parabolic equations in three space dimensions with mixed derivatives. The Computer Journal, 14:295-300, 1971. (with S. McKee).
  46. Forbidden shapes in the finite element method. J. Inst. Maths Applics., 8:260-269, 1971. (with G. M. Phillips and E. L. Wachspress).
  47. Variational principles and the finite element method in partial differential equations. Proc. Roy. Soc. London, A323:211-217, 1971.
  48. On the structure of ADI and LOD difference methods. J. Inst. Maths Applics., 9:80-90, 1972. (with A. R. Gourlay).
  49. Construction of basis functions in the finite element method. BIT, 12:81-89, 1972. (with G. M. Phillips).
  50. Basis functions for curved elements in the finite element method. In Proc. Second Manitoba Conf. on Num. Math., pages 35-50, 1972.
  51. An introduction to the mathematics of the finite element method. In J. R. Whiteman, editor, The Mathematics of Finite Elements and Applications I, pages 37-58. Academic Press, 1972.
  52. Variational principles and the finite element method. J. Inst. Maths Applics., 9:378-389, 1972.
  53. The construction of basis functions for curved elements in the finite element method. J. Inst. Maths Applics., 10:382-393, 1972. (with R. J. Y. McLeod).
  54. An exact boundary technique for improved accuracy in the finite element method. J. Inst. Maths Applics., 12:355-362, 1973. (with J. A. Marshall).
  55. Variational principles-a survey. In J. G. Gram, editor, Numerical Solution of Partial Diffential Equations, NATO Advanced Study Series, pages 17-23. D. Reidel Press, 1973.
  56. Element types and base functions. In J. G. Gram, editor, Numerical Solution of Partial Diffential Equations, NATO Advanced Study Series, pages 107-150. D. Reidel Press, 1973.
  57. Curved elements in the finite element method. In G. A. Watson, editor, Numerical Solution of Differential Equations, pages 89-104. Springer Verlag, 1973. (with R. J. Y. McLeod).
  58. Numerical analysis. In Encyclopaedia Brittanica, pages 381-392. 1974.
  59. Matching of essential boundary conditions in the finite element method. In J. J. H. Miller, editor, Topics in Numerical Analysis II, pages 109-120. Academic Press, 1974. (with J. A. Marshall).
  60. Curved boundaries in the finite element method. In J. Albrecht and L. Collatz, editors, Finite Elemente und Differenzverfahren, volume 28 of ISNM, pages 71-90. Birkhauser Verlag, 1975.
  61. The use of parabolic arcs in matching curved boundaries in the finite element method. J. Inst. Maths Applics., 16:139-246, 1975. (with R. J. Y. McLeod).
  62. Basis functions for curved elements in the mathematical theory of finite elements. In J. R. Whiteman, editor, The Mathematics of Finite Elements and Applications II, pages 43-58. Academic Press, 1975.
  63. Finite element methods for second order differential equations with significant first derivatives. Int. J. Numer. Meth. Engng., 10:1389-1396, 1976. (with I. Christie, D. F. Griffiths and O. C. Zienkiewicz).
  64. Finite element methods in conduction-convection problems. In J. Albrecht and L. Collatz, editors, Numerische Behandlung von Differentialgleichungen, volume 31 of ISNM, pages 171-179. Birkhauser Verlag, 1976.
  65. Exact control of a parabolic differential equation using an implicit Runge-Kutta method. J. Inst. Maths Applics., 18:9-14, 1976. (with P. J. Harley).
  66. Finite element methods in time dependent problems. In D. A. H. Jacobs, editor, The State of the Art in Numerical Analysis, pages 671-692. Academic Press, 1976.
  67. Generalized Galerkin methods for second order equations with significant first derivatives. In G. A. Watson, editor, Numerical Analysis, Dundee, pages 90-104. Springer, 1977. (with D. F. Griffiths).
  68. An upwind finite element scheme for two-dimensional convective transport equation. Int. J. Numer. Meth. Engng., 11:131-143, 1977. (with J. C. Heinrich, P. S. Huyakorn and O. C. Zienkiewicz).
  69. A finite element collocation method for the exact control of a parabolic problem. Int. J. Numer. Meth. Engng., 11:345-353, 1977. (with P. J. Harley).
  70. Computable finite element error bounds for Poisson's equation. Int. J. Numer. Meth. Engng., 11:593-603, 1977. (with R. E. Barnhill, J. H. Brown and N. McQueen).
  71. Upwinding of high order Galerkin methods in conduction-convection problems. Int. J. Numer. Meth. Engng., 12:1764-1771, 1978. (with I. Christie).
  72. Blending interpolants in the finite element method. Int. J. Numer. Meth. Engng., 12:77-83, 1978. (with J. A. Marshall).
  73. The parabolic-hyperbolic interface in conduction-convection problems. In I. Marek, editor, Proc. Fourth Symposium on Basic Problems in Numerical Mathematics, pages 141-151. Czech Academy of Sciences, 1978. (with F. Lawlor).
  74. Semi-discrete generalised Galerkin methods for time-dependent conduction-convection problems. In J. R. Whiteman, editor, The Mathematics of Finite Elements and Applications III, pages 19-35. Academic Press, 1978.
  75. Finite difference/finite element methods at the parabolic-hyperbolic interface. In P. W. Hemker and J. J. H. Miller, editors, Numerical Analysis of Singular Perturbation Problems, pages 339-361. Academic Press, 1978. (with I. Christie).
  76. Blending interpolants in the finite element method. Int. J. Numer. Meth. Engng., 12:77-83, 1978. (with J. A. Marshall).
  77. An analysis of a cubic isoparametric transformation. Int. J. Numer. Meth. Engng., 12:1587-1595, 1978. (with G. Woodford and R. J. Y. McLeod).
  78. Upwinding of high order Galerkin methods in conduction-convection problems. Int. J. Numer. Meth. Engng., 12:1764-1771, 1978. (with I. Christie).
  79. Semi-discrete generalized Galerkin methods for time-dependent conduction-convection problems. In J. R. Whiteman, editor, The Mathematics of Finite Elements and Applications III, pages 19-34. Academic Press, 1979. (with D. F. Griffiths).
  80. On generating upwind finite elements. In T. J. R. Hughes, editor, Finite Elements for Convection Dominated Flows, AMD vol 34, pages 91-105, New York, 1979. ASME. (with D. F. Griffiths).
  81. A piecewise parabolic C1 approximation technique for curved boundaries. Computers and Math. with Applics., 5:277-284, 1979. (with R. J. Y. McLeod).
  82. Advantages of cubics for approximating element boundaries. Computers and Math. with Applics., 5:321-327, 1979.
  83. Analysis of generalised Galerkin methods in the numerical solution of elliptic equations. Math. Meth. in the Appl. Sci., 1:3-15, 1979. (with R. S. Anderssen).
  84. Analysis of error growth for explicit difference schemes in conduction convection problems. Int. J. Numer. Meth. Engng., 15:1075-1081, 1980. (with I. Christie and D. F. Griffiths).
  85. Upwinding by Petrov-Galerkin methods in convection-diffusion problems. J. Comp. and Appl. Math., 6:219-228, 1980. (with D. F. Griffiths).
  86. Finite element Galerkin methods for convection-diffusion and reaction-diffusion. In L. S. Frank O. Axelsson and A. van der Sluis, editors, Analytical and Numerical Approaches to Asymptotic Problems in Analysis. North Holland, 1981. (with D. F. Griffiths and A. F. Meiring).
  87. A comparison of finite element error bounds for Poisson's equation. IMA J. Num. Anal., 1:95-103, 1981. (with R. E. Barnhill and J. H. Brown).
  88. Product approximation for non-linear problems in the finite element method. IMA J. Num. Anal., 1:253-266, 1981. (with I. Christie, D. F. Griffiths and J. M. Sanz-Serna).
  89. The stability of a Petrov-Galerkin method for the periodic convection-diffusion problem. Math. Num. Sinica, 4:138-146, 1982. (with D. F. Griffiths and Guo Pen-Yu).
  90. Finite element studies in reaction-diffusion. In J. R. Whiteman, editor, The Mathematics of Finite Elements and Applications IV, pages 17-36. Academic Press, 1982. (with V. S. Manoranjan).
  91. A moving Petrov-Galerkin method for transport equations. Int. J. Numer. Meth. Engng., 18:1321-1336, 1982. (with B. M. Herbst and S. W. Schoombie).
  92. A numerical study of the Belousov-Zabotinskii reaction using Galerkin finite element methods. J. Math. Biol., 16:251-260, 1983. (with V. S. Manoranjan).
  93. The stability of the Petrov-Galerkin method for the initial boundary value problem for the convection-diffusion equation. Acta Math Sinica, 26:54-64, 1983. (with Guo Ben Yu).
  94. Equidistributing principles in moving finite element methods. J. Comp. and Appl. Math., 9:377-389, 1983. (with B. M. Herbst and S. W. Schoombie).
  95. A self-adaptive difference scheme for the nonlinear Schrödinger equation. Arab Gulf J. of Scientific Research, 1:461-473, 1983. (with J. Ll. Morris).
  96. A numerical study of the Belousov-Zhabotinskii reaction using Galerkin finite element methods. J. Math Biology, 16:251-260, 1983. (with V. S. Manoranjan).
  97. Recent developments in the application of finite element methods to current problems in applied mathematics. In R. Alani, editor, First Int. Conf. in Math., pages 1-26. Arab Bureau of Education for the Gulf States, 1983.
  98. A numerical study of the nonlinear Schrödinger equation. Comp. Meth. Appl. Mech. Engng., 45:177-216, 1984. (with D. F. Griffiths and J. Ll. Morris).
  99. Finite element studies of solitons. In R. W. Lewis, P. Bettess, and E. Hinton, editors, Numerical Methods in Coupled Systems, pages 465-489. John Wiley & Sons, 1984. (with S. W. Schoombie).
  100. Generalized Petrov-Galerkin methods for the numerical solution of Burger's equation. J. Comp. Phys., 20:1273-1289, 1984. (with B. M. Herbst, D. F. Griffiths and S. W. Schoombie).
  101. Numerical solutions of the good Boussinesq equation. SIAM J. Sci. Stat. Comp., 5:946-957, 1984. (with V. S. Manoranjan and J. Ll. Morris).
  102. Curved elements. In D. F. Griffiths, editor, The Mathematical Basis of the Finite Element Method, IMA Conference Series, pages 157-168. Oxford University Press, 1984.
  103. Nonconforming elements. In D. F. Griffiths, editor, The Mathematical Basis of the Finite Element Method, pages 41-70. Oxford University Press, 1984. (with D. F. Griffiths).
  104. Recent developments in the finite element method. In Computational Techniques and Applications, pages 2-14. North Holland Press, 1984.
  105. Bifurcation studies in reaction-diffusion. J. Computational and Applied Mathematics, 11:27-37, 1984. (with V. S. Manoranjan, B. D. Sleeman and Guo Ben Yu).
  106. Numerical studies of bifurcation and pulse evolution in mathematical biology. In J. R. Whiteman, editor, The Mathematics of Finite Elements and Applications V, pages 175-191. Academic Press, 1985. (with V. S. Manoranjan).
  107. On the stability of the nonlinear Schrödinger equation. J. Comp. Phys., 60:263-281, 1985. (with B. M. Herbst and J. A. C. Weideman).
  108. Numerical experience with the nonlinear Schrödinger equation. J. Comp. Phys., 60:282-305, 1985. (with B. M. Herbst and J. Ll. Morris).
  109. A numerical study of chaos in a reaction-diffusion equation. Num. Methods PDEs., 1:13-23, 1985. (with J. C. Bruch Jr).
  110. Adaptive grids in Petrov-Galerkin computations. In Accuracy Estimates and Adaptive Refinements in Finite Element Computations, pages 315-324. John Wiley & Sons, Chichester, 1986. (with B. M. Herbst).
  111. Analysis of a nonlinear difference scheme in reaction-diffusion. Numer. Math., 49:511-527, 1986. (with Guo Ben-Yu).
  112. Beyond the linearised stability limit in nonlinear problems. In D. F. Griffiths and G. A. Watson, editors, Numerical Analysis Proceedings, Dundee, pages 140-156. Pitman Research Notes in Mathematics Series, Vol 140, 1986. (with D. F. Griffiths).
  113. On nonlinear instabilities in leap-frog finite difference schemes. J. Comp. Phys., 67:372-395, 1986. (with D. M. Sloan).
  114. Spatial effects in a two-dimensional model of the budworm-balsam fir ecosystem. Comp. and Math. with Applics., 12B:1117-1132, 1986. (with Guo Ben-Yu and B. D. Sleeman).
  115. On a one-dimensional difference scheme in reaction diffusion. J. Comp. Math., 5:191-202, 1987. (with Guo Ben-Yu and Chen Sui-Yang).
  116. Period doubling bifurcations in non-linear difference equations. SIAM J. Sci. Stat. Comp., 9:543-557, 1988. (with B. D. Sleeman, D. F. Griffiths and P. D. Smith).
  117. Periodic structure beyond a Hopf bifurcation. Commun. Appl. Numer. Meth., 4:263-272, 1988. (with G. Stein and M. Maritz).
  118. Nonlinear instability in long time calculations of a partial difference equation. In Comp. Meth in Water Resources VII, pages 153-161. Elsevier, 1988.
  119. Nonlinear diffusion and stable period 2 solutions of a discrete reaction-diffusion model. J. Comp. and Appl. Math., 25:363-372, 1989. (with S. W. Schoombie).
  120. Spurious behaviour and nonlinear instability in discretised partial differential equations. In D. S. Broomhead and A. Iserles, editor, Proceedings of Dynamics of Numerics and Numerics of Dynamics, pages 215-242. Cambridge University Press, 1990. (with D. F. Griffiths).
  121. Spatial patterning of the Spruce budworm in a circular region. Science in China (Series A), 34:676-688, 1991. (with Guo Ben-Yu and B. D. Sleeman).
  122. Numerical solution of Hamiltonian systems in reaction-diffusion by symplectic difference schemes. J. Comp. Phys., 95:339-358, 1991. (with B. A. Murray and B. D. Sleeman).
  123. Attractors in long time solutions of discretised nonlinear systems. In T. F. Russell and R. E. Ewing, editors, Numerical Methods in Water Resources, pages 107-120. Elsevier Applied Science, 1992.
  124. Bifurcation studies in long time solutions of discrete mode in reaction diffusion. University of Dundee Report NA/136, 1992. (with A. R. Gardiner).
  125. Periodic bifurcations of an explicit discretisation of the Ginzburg-Landau equation. University of Dundee Report NA/137, 1992. (with A. R. Gardiner).
  126. Unstable attractors of a discretised inviscid Burgers equation. University of Dundee Report NA/139, 1992. (with A. R. Gardiner).
  127. The influence of dispersion on the inviscid Burgers equation. University of Dundee Report NA/142, 1992. (with A. R. Gardiner).