Doctor of Philosophy (PhD)
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 lnd+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.
Document Availability at the Time of Submission
Release the entire work immediately for access worldwide.
Huang, Xu, "Exponentially Convergent Generalized Finite Element Method for Multi-scale Problems" (2014). LSU Doctoral Dissertations. 3105.