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Johnson - Numerical Solution of Partial Differential Equations by the Finite Element Method

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Johnson Numerical Solution of Partial Differential Equations by the Finite Element Method
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    Numerical Solution of Partial Differential Equations by the Finite Element Method
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An accessible introduction to the finite element method for solving numeric problems, this volume offers the keys to an important technique in computational mathematics. Suitable for advanced undergraduate and graduate courses, it outlines clear connections with applications and considers numerous examples from a variety of science- and engineering-related specialties. 1987 edition.

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Table of Contents References Ad Adams R A Sobolev Spaces Academic - photo 1
Table of Contents

References

[Ad] Adams, R A. Sobolev Spaces, Academic Press, 1975.

[Ax] Axelsson, O. A class of iterative methods for finite element equations. Comp. Math. in Appl. Mech. and Eng. 9 (1976).

[BM] Babuska, I., and Miller, A. A feedback finite element method with a posteriori error estimates: Part I. The finite element method and some basic properties of the a posteriori estimator, Comp. Meth. Appl. Mech. Engng. 61 (1987).

[BR] Babuska, I., and Rheinboldt, W. C. Error estimates for adaptive finite element computations, SIAM J. of Num. Anal. 15(1978), p 736754.

[Ba] Bank, R. PLTMG Users Guide, Math. Dept., Univ. of Californa at San Diego, 1981.

[BD] Bank, R. E., and Dupont, T. An optimal order process for solving elliptic finite element equations, Math. Comp. 36 (1981), 3551.

[Be] Bercovier, M., Berold, G., and Hasbani, Y. LSD/FEM. A Library for software development in the finite element method, The Hebrew University of Jerusalem.

[BPHL] Bercovier, M., Pironneau, O., Hasbani Y., and Livne, E. Characteristic and finite element methods applied to the equations of fluids, Proc. MAFELAP 81, J. R. Whiteman ed., Academic Press, London (1982), 471478.

[Bra] Brandt, A. Multi-level adaptive solutions to boundary value problems, Math. Comp. 31 (1977), 333390.

[Br] Brezzi, F. On the existence, uniqueness and approximation of saddle point problems arising from Lagrangian multipliers, RAIRO Num. Anal. 8(1974), p 129-151.

[BP] Brezzi F., Pitkranta J. On the stabilization of finite element approximations of the Stokes equations, Report MAT-A219, Helsinki University of Technology, Mathematics department, 1984.

[BH] Brooks, A., and Hughes T. Streamline upwind/Petrov-Galerkin formulations for convection dominated flows with particular emphais on the incompressible Navier-Stokes equations, Comp. Meth. Appl. Mech. Engng. 32 (1982), 199-259.

[Ci] Ciarlet, P. G. The Finite Element Method For Elliptic Problems, North Holland, 1978.

[CM] CLUB MODULEF, A library of computer procedures for finite element analysis, INRIA, Rocquencourt, France.

[DR] Douglas, J. Jr., and Russel, T. Numerical methods for convection dominated diffusion problems based on combining the method of characteristics with finite element or finite difference procedures, SIAM J. Numer. Anal. 19 (1982), 871885.

[DS] Dupont, T., and Scott, R. Polynomial approximation of functions in Sobolev spaces, Math. Comp. 34 (1980), p 441463.

[DL] Duvaut, G., and Lions, J. L. Les Inquations en Mcanique et en Physique, Dunod, 1972.

[ET] Ekeland, I., and Temam, R. Convex Analysis and Variational Problems, North-Holland, 1976.

[E] Eriksson, K. Adaptive finite element methods based on optimal error estimates for linear elliptic problems, to appear in Math. Comp.

[EJ1] Eriksson, K., and Johnson, C. Error estimates and automatic time step control for non-linear parabolic problems I, SIAM J. Numer. Anal. 24 (1987), 1222.

[EJ2] Eriksson K., and Johnson, C. An adaptive method for linear elliptic problems, Math. Comp. 50 (1988) p 361383.

[EJL] Eriksson, K., Johnson, C., and Lennblad, J. Adaptive finite element methods for parabolic problems I: A linear model problem, to appear in SIAM J. Numer. Anal.

[EJT] Eriksson, K., Johnson, C., and Thomee, V. Time discretization of parabolic problems by the discontinuous Galerkin method, RAIRO, MAN. 19 (1985), 611643.

[Fi] FIDAP, Fluid Dynamics Analysis Package, Fluid Dynamics International, Inc., 1600 Orrington Avenue, Suite 505, Evanston, Illinois 60201.

[F] Friedrichs, K. O. Comm. Pure and Appl. Math. 11 (1958).

[Ge] George, A. Nested dissection of regular finite element mesh, Siam J. Num. Anal. 11, 1973, 345363.

[GR] Girault, V., and Raviart, P. A. Finite Element Approximation of the Navier-Stokes Equations. Lecture Notes in Mathematics, 749, Springer, 1979.

[G] Glowinski, R. Numerical Methods for Non-linear Variational Problems, Springer Series in Computational Physics, Springer, 1983.

[GLT] Glowinski, R., Lions, J. L., and Tremolieres, R. Numerical Analysis of Variational Inequalities, North-Holland, 1981.

[Hac] Hackbusch, W. Multigrid Methods and Applications, Springer Series in Computational Mathematics 4, Springer, 1985.

[Han] Hansbo, P. Finite element procedures for conduction and convection problems, Licenciat Thesis, Dept. of Structural Mechanics, Chalmers Univ. of Technology 1986.

[HB1] Hughes, T. J., and Brooks, A. A multidimensional upwind scheme with no crosswind diffusion, in AMD vol 34, Finite element methods for convection dominated flows, Hughes T. J. (ed): ASME, NY 1979.

[HB2] Hughes, T. J., and Brooks, A. A theoretical framework for Petrov-Galerkin methods with discontinuous weighting functions. Applications to the streamline-upwind procedure. Finite elements in fluids vol 4, ed. Gallagher, Wiley 1982.

[HFB] Hughes, T. J., Franca L., and Balestra M. A new finite element formulation for computational fluid dynamics: V. Circumventing the Babuska-Brezzi condition: A stable Petrov-Galerkin formulation of the Stokes problem accomodating equal-order interpolations, to appear in Comp. Meth. Appl. Mech. Engng.

[HFM] Hughes, T. J., Franca, L., and Mallet, M. A new finite element formulation for computational fluid dynamics: I. Symmetric forms of the compressible Euler and Navier-Stokes equations and the second law of thermodynamics, Comp. Meth. in Appl. Mech. Eng. 54 (1986), 223234.

[HM1] Hughes, T. J., and Mallet M. A new finite element formulation for computational fluid dynamics: III. The general streamline operator for multidimensional advective-diffusive systems, Comp. Meth. Appl. Mech. 58 (1986), 305328.

[HM2] Hughes, T. J., and Mallet M. A new finite element formulation for computational fluid dynamics: IV. A discontinuity-capturing operator for multidimensional advective-diffusive systems, Comp. Meth. Appl. Mech. 58 (1986), 329336.

[HMM] Hughes, T. J., Mallet M., and Mizukami A. A new finite element method for computational fluid dynamics: II. Beyond SUPG, Comp. Math. in Appl. Mech. 54 (1986), 341-355.

[I] Irons, B. A frontal solution program for finite element analysis, Int. J. Num. Meth. Eng. 2 (1970), p 532.

[J1] Johnson C. Numerical solution of partial differential equations by the finite element method, Studentlitteratur 1980 (in Swedish).

[J2] Johnson, C. Finite element methods for convection-diffusion problems, in Computing methods in applied sciences and engineering, ed R. Glowinski, J-L. Lions, North Holland 1982.

[J3] Johnson, C. Error estimates and automatic time step control for numerical methods for stiff ordinary differential equations, SIAM J. Numer. Anal. 25 (1988), p 908926.

[J4] Johnson, C. Streamline diffusion methods for problems in fluid mechanics, in Finite Elements in Fluids VI, Wiley, 1986.

[JN] Johnson. C., and Nedelec J. C. On the coupling of boundary integral and finite element methods, Math. Comp. 35 (1980), 10631079.

[JNT] Johnson, C., Nie, Y. Y., and Thome, V. An a posteriori error estimate and automatic time step control for a backward Euler discretization of a parabolic problem, Technical report 1985-23, Math. Dept., Chalmers Univ. of Technology, to appear in SIAM J. Numer. Anal.

[JN] Johnson, C., and Nvert U. An analysis of some finite element methods for advection-diffusion problems, in Axelsson, Frank, Van der Sluis (eds), Analytical and numerical approaches to asymptotic problems in analysis, North Holland, 1981.

[JNP] Johnson, C., Nvert, U., and Pitkaranta, J. Finite element methods for linear hyperbolic problems. Comp. Meth. in Appl. Mech. Engng. 45 (1984), p 285312.

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