Thursday, November 16, 2023 - 09:45 in V2-210/216
Scaling-robust built-in a posteriori error estimation for discontinuous least-squares finite element methods
A talk in the BI.discrete Workshop series by
Philipp Bringmann from Wien
| Abstract: |
Least-squares schemes solve PDEs by considering an artificial energy functional consisting of the sum of the residuals in squared L2 norms. The least-squares finite element methods (LSFEMs) minimize this least-squares functional over discrete finite element subspaces of the corresponding Sobolev spaces. A convincing feature of this class of methods is the built-in a posteriori error estimator for any conforming discretization. In order to generalize this property to discontinuous finite element ansatz functions, the talk presents a least-squares principle on piecewise Sobolev functions for the solution of the Poisson model problem in 2D with mixed boundary conditions. It allows for various discretizations including standard piecewise polynomial ansatz spaces on triangular and polygonal meshes. A suitable weighting of the residuals in the least-squares functionals enables an analysis being robust with respect to the size of the domain. Numerical experiments exhibit optimal convergence rates of the adaptive mesh-refining algorithm for various polynomial degrees.
Within the CRC this talk is associated to the project(s): A7, B3, B7 |
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