Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
5776628 | Applied Numerical Mathematics | 2017 | 32 Pages |
Abstract
In this paper, we develop a priori estimates for the convergence of outputs, output error estimates, and localizations of output error estimates for Galerkin finite element methods. Output error estimates for order p finite element solutions are constructed using the Dual-Weighted Residual (DWR) method with a higher-order pâ²>p dual solution. Specifically, we analyze these DWR estimates for Continuous Galerkin (CG), Discontinuous Galerkin (DG), and Hybridized DG (HDG) methods applied to the Poisson problem. For all discretizations, as hâ0, we prove that the output and output error estimate converge at order 2p and 2pâ² (assuming sufficient smoothness), while localizations of the output and output error estimate converge at 2p+d and p+pâ²+d. For DG, the results use a new post processing for the error associated with the lifting operator. For HDG, these rates improve an additional order when the stabilization is based upon an O(1) length scale.
Related Topics
Physical Sciences and Engineering
Mathematics
Computational Mathematics
Authors
Hugh A. Carson, David L. Darmofal, Marshall C. Galbraith, Steven R. Allmaras,