Question

This class of methods is contrasted with another class in which the differential operator is approximated with difference quotients. For 10 points each:
[10m] Name this class of numerical methods that solve a PDE by defining a discrete mesh and solving the problem on each component. The stiffness matrix is computed in this subclass of the Galerkin method.
ANSWER: finite element methods [accept finite element analysis or FEM or FEA; reject “finite difference method” or “finite volume method” or “FDM” or “FVM”]
[10e] Finite element methods use an operator named for this process, in which data are estimated at points between known data points.
ANSWER: interpolation [or interpolating; accept interpolation operator]
[10h] After discretizing, the existence of a solution to the adjoint problem is guaranteed by a theorem named for this mathematician, which also underpins bra-ket notation. This mathematician’s brother is the alphabetically first namesake of a theorem about interpolating operators on L-p (“big-L-P”) spaces.
ANSWER: Frigyes Riesz (“FREE-jesh REESS”) [accept Riesz representation theorem or Riesz-Fréchet representation theorem or Riesz–Thorin interpolation theorem; reject “Marcel Riesz”]
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Summary

2025 ACF Nationals04/19/2025Y2413.75100%38%0%

Data

Arizona StateOttawa010010
Georgia StateBritish Columbia010010
Chicago BMIT010010
Columbia ANorthwestern010010
Columbia BRIT010010
MichiganCornell B1010020
Georgia TechCornell A010010
UC Berkeley AIllinois A1010020
Illinois BVirginia1010020
MinnesotaIowa State010010
Johns HopkinsHarvard1010020
StanfordNorth Carolina A1010020
MarylandNorth Carolina B010010
VanderbiltOhio State010010
FloridaPenn State1010020
RutgersIndiana010010
Waterloo AToronto A010010
Virginia TechToronto B010010
Toronto CTexas010010
LSEUC Berkeley B010010
UCFWinona State1010020
Chicago AWUSTL A1010020
YaleWUSTL B010010
Waterloo BNYU1010020