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4.1 The Galerkin Method - Optional

This section can be bypassed by students who have not encountered finite element, finite difference, or boundary element methods before. It does, however, provide a unifying basis from which the finite and boundary element and finite difference methods can be derived.

The problem posed in (1) can be solved using any of the aforementioned approximation schemes. One technique which addresses three of the previously mentioned techniques (FD, FE, and BE) can be derived by the Galerkin method. The Galerkin method is one of the most widely used methods for discretizing elliptic boundary value problems such as (1) and for treating the spatial portion of time-dependent parabolic problems, which are common in models of cardiac wave propagation. While the Galerkin technique is not essential to the application of any of the techniques, it provides for a unifying bridge between the various numerical methods.