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Full-Text Articles in Physical Sciences and Mathematics
Finite Element Method Analysis Of Resonant Cavity For Whispering Gallery Acoustic Sensing Microscopy, Thanh N.D. Le, Ha Tran, Andres H. La Rosa
Finite Element Method Analysis Of Resonant Cavity For Whispering Gallery Acoustic Sensing Microscopy, Thanh N.D. Le, Ha Tran, Andres H. La Rosa
Student Research Symposium
Whispering Gallery Acoustic Sensing (WGAS) has been studied by Department of Physics at Portland State University as a mean of controlling sample to probe distance in tuning-folk-based scanning probe microscopy (TF-SPM). WGAS uses the microscope frame as a resonance acoustic cavity. The setup shows high potential because of high-quality factor nature of acoustic cavity as well as using mechanical motions of the TF itself instead of electrical signals. However, the analytic solution of the eigenfrequencies of the current microscope frame is very complex due to the asymmetric geometry. The purpose of this study is to use finite element method to …
Some Remarks On Interpolation And Best Approximation, Randolph E. Bank, Jeffrey S. Ovall
Some Remarks On Interpolation And Best Approximation, Randolph E. Bank, Jeffrey S. Ovall
Mathematics and Statistics Faculty Publications and Presentations
Sufficient conditions are provided for establishing equivalence between best approximation error and projection/interpolation error in finite-dimensional vector spaces for general (semi)norms. The results are applied to several standard finite element spaces, modes of interpolation and (semi)norms, and a numerical study of the dependence on polynomial degree of constants appearing in our estimates is provided.