This talk is sponsored by Baylor's Department of Mathematics and CASPER. B.E.A.R.S., with permission, has chosen to participate.
Refreshments: 3:00 PM in Room 318 Sid Richardson
Abstract:
Abstract: Finite element approximations for the eigenvalue problem of the
Laplace operator will be discussed. A gradient recovery scheme is proposed to
enhance the finite element solutions of the eigenvalues. By reconstructing the
numerical solution and its gradient, it is possible to produce more accurate
numerical eigenvalues. Furthermore, the recovered gradient can be used to form
a posteriori error estimator to guide an adaptive mesh refinement. Therefore, this
method works not only for structured meshes, but also for unstructured and
adaptive meshes.
Our theoretical results will be numerically verified. Furthermore, the method can
be applied to general second-order elliptic operators, fourth-order and higher order
partial differential operators.
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