FEA-The Finite-dimensional Weak Form

In this course, we discuss how the infinite-dimensional weak form of a 1D linear elliptic partial differential equation (PDE) can be transformed to a finite-dimensional weak form, which forms the basis of the finite element method. We discuss basic Hilbert spaces, which are functional spaces in which acceptable solutions to the weak form exist. We also discuss basis functions and how the finite-dimensional weak form can be written as a sum over the finite subdomains (or elements) of the problem. This course was developed by Prof. Krishna Garikipati and Dr. Gregory Teichert at the University of Michigan, in partnership with Ansys.

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