Exponentially Convergent Generalized Finite Element Method for Multi-scale Problems

Identifier

etd-03312015-144425

Author

Xu Huang, Louisiana State University and Agricultural and Mechanical CollegeFollow

Degree

Doctor of Philosophy (PhD)

Department

Mathematics

Document Type

Dissertation

Abstract

The overall approach I take in the thesis falls into the category of multiscale finite element methods(MsFEM). I work to identify a new class of local approximation spaces with good approximation properties. This is carried out for the equilibrium problem of linear elasticity. The choice of local approximation spaces is motivated by the kolmogorov n-width. Part of my thesis work develops an estimate to show that it is possible to achieve a local approximation error of ô with respect to the energy norm using at most ln^d+1 &frac1ô local basis functions. The global approximation error ôis controlled by the local approximation error and I recover a global approximation to the actual solution with exponential accuracy.

Date

2014

Document Availability at the Time of Submission

Release the entire work immediately for access worldwide.

Recommended Citation

Huang, Xu, "Exponentially Convergent Generalized Finite Element Method for Multi-scale Problems" (2014). LSU Doctoral Dissertations. 3105.
https://repository.lsu.edu/gradschool_dissertations/3105

Committee Chair

Lipton, Robert

DOI

10.31390/gradschool_dissertations.3105