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Estimates of error in finite element approximate solutions to problems in linear thermoelasticity. I: Computationally coupled numerical schemes. (English) Zbl 0494.73071


MSC:

74S05 Finite element methods applied to problems in solid mechanics
74F05 Thermal effects in solid mechanics
65M15 Error bounds for initial value and initial-boundary value problems involving PDEs
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[1] Chou, S.-I., & C.-C. Wang, Error estimates of finite element approximations for problems in linear elasticity (in three parts). Arch. Rational Mech. Anal. 72, 41–60, 155–174 (1979), 73, 159–182 (1980). · Zbl 0418.73068
[2] Nickell, R. E., & J. L. Sackman, Approximate solutions in linear coupled thermoelasticity, J. Appl. Mech. 35, 255–266 (1968). · Zbl 0159.55605
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[8] Ciarlet, P. G., & P. A. Raviart, General Lagrange and Hermite interpolation in R n with applications to finite element methods, Arch. Rational Mech. Anal. 46, 177–199 (1972). · Zbl 0243.41004 · doi:10.1007/BF00252458
[9] Schultz, M. H., L 2 error bounds for the Rayleigh-Ritz-Galerkin method, SIAM J. Numer. Anal. 8, 737–748 (1971). · Zbl 0285.65070 · doi:10.1137/0708067
[10] Nickell, R. E., & J. L. Sackman, Variational principles for linear coupled thermoelasticity, Q. Appl. Math. 26, 11–26 (1968). · Zbl 0165.27504
[11] Dafermos, C. M., On the existence and the asymptotic stability of solutions to the equations of linear thermoelasticity, Arch. Rational Mech. Anal. 29, 241–271 (1968). · Zbl 0183.37701 · doi:10.1007/BF00276727
[12] Nowacki, W., Dynamic problems of thermoelasticity, Noordhoff International Publishers 1976. · Zbl 0354.73009
[13] Nowinski, J. L., Theory of thermoelasticity with applications, Noordhoff International Publishers 1978. · Zbl 0379.73004
[14] Chou, S.-I., Galerkin approximations on linear elastostatics, elastodynamics, and thermoelastodynamics, Ph. D. Thesis, Rice University 1972.
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