Seminars & Events

Mathematics and Computer Science Division
" $hp$-Adaptive Finite Elements and Approximate Newton-Krylov Solver"

DATE: March 23, 2011
TIME: 10:30 AM - 11:30 AM
SPEAKER: Hieu Nguyen, LANS Postdoc Interviewee
LOCATION: Building 240 Seminar Room 4301, Argonne National Laboratory
HOST: Barry Smith

Description:
First, we will describe a new approach to the $p$ and $hp$ versions of finite element method. Our approach is characterized by the use of nodal basis functions, and a posteriori error estimates based on derivative recovery. The special basis functions defined for transition elements allow us to accommodate elements of different degrees, avoid hanging nodes and maintain the continuity of the finite element space. Our error estimates are very attractive as they are robust and independent of the PDE.

Second, we will discuss the use of an approximate Newton's method in conjunction with GMRES to solve large nonlinear systems in IWFM, a water resources management and planning (finite element) model developed by California State Department of Water Resources. Strategies to adaptively control GMRES accuracy and formulate damping factors are proposed.

Numerical results will be provided in both parts of the talk.

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