[00461] hp/Spectral Element Methods for Elliptic Boundary Layer Problems
Session Time & Room : 5D (Aug.25, 15:30-17:10) @E709
Type : Contributed Talk
Abstract : Elliptic boundary layer problems arise in many applications including fluid dynamics, gas dynamics, plate and shell problems in structural mechanics, modeling of semiconductor devices and many more.
We propose a least-squares hp-spectral element method for 1D elliptic boundary layer problems. The regularity estimates are stated and the main stability theorem is obtained using non-conforming spectral element functions. For the hp-version we use a 3 element mesh which allows us to resolve the boundary layers completely by placing very thin needle like elements near the boundary layer and a coarse mesh away from the layer. Numerical scheme and error estimates are obtained which are robust i.e. independent of the boundary layer parameter and decay exponentially in terms of the degree of the approximating polynomials. Numerical results confirm convergence results with various combinations of the boundary layer thickness, degrees of the approximating polynomials, and layers in the mesh.
