Abstract
In this chapter, we briefly discuss some numerical methods for solving boundary value problems. These are the Galerkin method and its variants: the Petrov-Galerkin method and the generalized Galerkin method. In Section 9.4, we rephrase the conjugate gradient method, discussed in Section 5.6, for solving variational equations.
The Galerkin method provides a general framework for approximation of operator equations, which includes the finite element method as a special case. In this section, we discuss the Galerkin method for a linear operator equation in a form directly applicable to the study of the finite element method.
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© 2009 Springer-Verlag New York
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Atkinson, K., Han, W. (2009). The Galerkin Method and Its Variants. In: Theoretical Numerical Analysis. Texts in Applied Mathematics, vol 39. Springer, New York, NY. https://doi.org/10.1007/978-1-4419-0458-4_9
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DOI: https://doi.org/10.1007/978-1-4419-0458-4_9
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Publisher Name: Springer, New York, NY
Print ISBN: 978-1-4419-0457-7
Online ISBN: 978-1-4419-0458-4
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