Wednesday, September 25, 2019 - 14:40 in H10
Discretization of Elliptic Equations with the Finite Element Method and Randomized Quadrature Formulas
A talk in the Keine Reihe series by
Raphael Kruse from TU Berlin
| Abstract: |
The implementation of the finite element method for linear elliptic partial dif-
ferential equations (PDE) requires to assemble the stiffness matrix and the load vector. In
general, the entries of this matrix-vector system are not known explicitly but need to be
approximated by quadrature rules. However, if the coefficient functions of the differential
operator or the forcing term are irregular, then standard quadrature formulas, such as the
barycentric quadrature rule, may not be reliable. In this talk we discuss the application of
two randomized quadrature formulas to the finite element method for such elliptic PDE with
irregular coefficient functions. We derive detailed error estimates for these methods, discuss
their implementation, and demonstrate their capabilities in several numerical experiments.
This talk is based on joint work with Nick Polydorides (U Edinburgh) and Yue Wu (U Oxford).
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