Luke Owens, University of South Carolina


A W-Cycle Multigrid Algorithm for a New NIPG Method

Abstract:  We introduce a new non-symmetric interior penalty discontinuous Galerkin (NIPG) method for solving elliptic boundary value problems. The new NIPG method introduced has h-optimal error estimates in both the energy norm and L2 norm. Also, although the resulting global stiffness matrix has a condition number of order h^-4, there is a simple preconditioner that reduces the condition number to h^-2. This is a significant advantage when designing a good smoothing procedure for multigrid algorithms. We then prove that there is a bound (<1) for the contraction number of the W-cycle algorithm, which is independent of the mesh level, for an appropriately chosen number of smoothing steps.

Advisor: Susan Brenner (USC and LSU)