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Full-Text Articles in Physical Sciences and Mathematics
Material Tensors And Pseudotensors Of Weakly-Textured Polycrystals With Orientation Measure Defined On The Orthogonal Group, Wenwen Du
Theses and Dissertations--Mathematics
Material properties of polycrystalline aggregates should manifest the influence of crystallographic texture as defined by the orientation distribution function (ODF). A representation theorem on material tensors of weakly-textured polycrystals was established by Man and Huang (2012), by which a given material tensor can be expressed as a linear combination of an orthonormal set of irreducible basis tensors, with the components given explicitly in terms of texture coefficients and a number of undetermined material parameters. Man and Huang's theorem is based on the classical assumption in texture analysis that ODFs are defined on the rotation group SO(3), which strictly speaking makes …
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 …