University of Minnesota
Aerospace Engineering and Mechanics
Spring 2000 Seminar Series
Error estimation and adaptive meshing in nonlinear dynamic problems
We present a general variational framework for mesh adaption in strongly
nonlinear, possibly dynamic, problems. We begin by showing that the solutions
of the incremental boundary value problem for a wide class of materials,
including nonlinear elastic materials, compressible newtonian fluids, and
viscoplastic solids, obey a minimum principle, provided that the constitutive
updates are formulated appropriately. This minimum principle can be taken as a
basis for asymptotic error estimation. In particular, we chose to monitor the
error of a lower-order projection of the finite element solution. The optimal
mesh size distribution then follows from a posteriori error indicators which
are purely local, i.e., can be computed element-by-element. We demonstrate the
robustness and versatility of the computational framework with the aid of
convergence studies and selected examples of application.
Friday, February 18, 2000
Refreshments served after the seminar in
227 Akerman Hall.
Disability accomodations provided upon request.
Contact Kristal Belisle, Senior