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Full-Text Articles in Physical Sciences and Mathematics
Numerical Methods And Algorithms For High Frequency Wave Scattering Problems In Homogeneous And Random Media, Cody Samuel Lorton
Numerical Methods And Algorithms For High Frequency Wave Scattering Problems In Homogeneous And Random Media, Cody Samuel Lorton
Doctoral Dissertations
This dissertation consists of four integral parts with a unified objective of developing efficient numerical methods for high frequency time-harmonic wave equations defined on both homogeneous and random media. The first part investigates the generalized weak coercivity of the acoustic Helmholtz, elastic Helmholtz, and time-harmonic Maxwell wave operators. We prove that such a weak coercivity holds for these wave operators on a class of more general domains called generalized star-shape domains. As a by-product, solution estimates for the corresponding Helmholtz-type problems are obtained.
The second part of the dissertation develops an absolutely stable (i.e. stable in all mesh regimes) interior …
A Posteriori Error Estimates For Surface Finite Element Methods, Fernando F. Camacho
A Posteriori Error Estimates For Surface Finite Element Methods, Fernando F. Camacho
Theses and Dissertations--Mathematics
Problems involving the solution of partial differential equations over surfaces appear in many engineering and scientific applications. Some of those applications include crystal growth, fluid mechanics and computer graphics. Many times analytic solutions to such problems are not available. Numerical algorithms, such as Finite Element Methods, are used in practice to find approximate solutions in those cases.
In this work we present L2 and pointwise a posteriori error estimates for Adaptive Surface Finite Elements solving the Laplace-Beltrami equation −△Γ u = f . The two sources of errors for Surface Finite Elements are a Galerkin error, and a …