The Galerkin Method and Its Variants
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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