Boundary Elements and the Biharmonic Equation
Possibly the most exciting development in applied numerical methods over the last fifteen years has been the popularization of “boundary element” methods. This modern engineering analysis technique has evolved from the much older mathematical subjects of integral equations, Green’s’ functions, and potential theory. The most graphic success of boundary elements have been in the analyses of scalar potential problems, most notably phenomena governed by Laplace’s equation (∇2ψ = 0) or the more general Poisson equation (∇2ψ = f). Other successful applications have been realized primarily in elliptic boundary value problems such as elastostatics analysis, steady-state wave propagation, etc.
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