Geodesic
On the convergence of the Galerkin method for coupled thermoelasticity problems
Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 46 (2006) no. 8, pp. 1462-1474

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The Cauchy problem for a system of two operator-differential equations is considered that is an abstract statement of linear coupled thermoelasticity problems. Error estimates in the energy norm for the semidiscrete Galerkin method as applied to the Cauchy problem are established without imposing any special conditions on the projection subspaces. By way of illustration, the error estimates are applied to finite element schemes for solving the coupled problem of plate thermoelasticity considered within the framework of the Kirchhoff linearized theory. The results obtained are also applicable to the case when the projection subspaces in the Galerkin method (for the original abstract problem) are the eigenspaces of operators similar to unbounded self-adjoint positive definite operator coefficients of the original equations. 
@article{ZVMMF_2006_46_8_a9,
     author = {S. E. Zhelezovsky},
     title = {On the convergence of the {Galerkin} method for coupled thermoelasticity problems},
     journal = {\v{Z}urnal vy\v{c}islitelʹnoj matematiki i matemati\v{c}eskoj fiziki},
     pages = {1462--1474},
     publisher = {mathdoc},
     volume = {46},
     number = {8},
     year = {2006},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZVMMF_2006_46_8_a9/}
}
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S. E. Zhelezovsky. On the convergence of the Galerkin method for coupled thermoelasticity problems. Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 46 (2006) no. 8, pp. 1462-1474. http://geodesic.mathdoc.fr/item/ZVMMF_2006_46_8_a9/