Abstract
The use of variational methods of the least squares type has been studied by many authors. They were first introduced for scalar elliptic equations by Bramble & Schatz [1]. This work was extended by Baker [2], who also treated the scalar case. Recent applications have stressed the importance of these ideas for systems. These include problems in acoustics involving the Helmholtz equation [3]–[4], transonic flow problems of the mixed elliptic-hyperbolic type [5]–[7] and elasto-plastic problems [8]. The analysis of these methods for the special case of second order systems is given in [9]–[10], and the goal of this paper is to extend these results to higher order systems.
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References
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Dedicated to Walter Noll on his sixtieth birthday
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© 1987 Springer-Verlag Berlin Heidelberg
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Fix, G.J., Stephan, E. (1987). On the Finite Element—Least Squares Approximation to Higher Order Elliptic Systems. In: Analysis and Thermomechanics. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-61598-6_17
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DOI: https://doi.org/10.1007/978-3-642-61598-6_17
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