11.56 Stay and Barocas (International Journal for Numerical Methods in Fluids, 2003) demonstrated a localized reduction technique called

“stitching” for hydrodynamic problems for which known analytical solution is available. They discussed the computational advantage of the coupled Stokes-Raynolds, using a fully-flooded deformable-roll coating example. The difference between the peak pressure calculated with GOMA (a full-Newton finite element program for free and moving boundary problems) and that calculated with coupled Stokes-Raynolds code (error in pressure) along with the stitch length (in cm), is recorded in table below. Also given are the CPU solve-times (in seconds) for the coupled Stokes-Raynolds code.

a Plot the error in pressure against the stitch length. Describe the nature of the relation.
b Plot the error in pressure against the CPU time. Describe the nature of the relation.
c Estimate both the relations using the leastsquares method.
d Assess the fit of each model using .

Transcribed Image Text:

Stitch CPU Stitch CPU Length Error Time Length Error Time 0.1 0.01 140 0.8 0.25 85 0.2 0.11 130 0.9 0.24 81 0.3 0.15 118 1.0 0.21 73 0.4 0.17 102 1.1 0.20 65 0.5 0.20 105 1.2 0.18 55 0.6 0.24 100 1.3 0.18 58 0.7 0.25 85 1.4 0.15 50