Monday, August 27 2018
11:00am - 12:00pm
Computational Mathematics Colloquium
Computational Mathematics Colloquium: When Point Boundary Conditions Are Meaningful
and When They Are Not, or
Why We Need Functional Analysis

A beam with point support is a common example in engineering textbooks. Likewise, the Laplace equation with Dirichlet boundary condition (think a thin, very flexible membrane) is a common example in numerical math. Point constraints are a favorite of user of computational mechanics software. Yet imposing the value of the solution of the Laplace equation at a point in 2D or 3D (but not in 1D) makes numerical models misbehave. Turns out the boundary value problem in 2D and higher does not make sense. The reasons lie in the basics of modern PDE theory and functional analysis. We present a gentle introduction to that, accessible to the nonspecialist.
Speaker:Jan Mandel
Affiliation:Department of Mathematical and Statistical Science, University of Colorado Denver
Location:ACAD 4018

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