Analysis of output-based error estimation for finite element methods

作者：Carson Hugh A; Darmofal David L; Galbraith Marshall C; Allmaras Steven R

来源：Applied Numerical Mathematics, 2017, 118: 182-202.

DOI：10.1016/j.apnum.2017.03.004

• Output functional estimation
• Finite element method
• Discontinuous Galerkin
• Hybridizable Discontinuous Galerkin

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 p' > 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 h -> 0, we prove that the output and output error estimate converge at order 2p and 2p' (assuming sufficient smoothness), while localizations of the output and output error estimate converge at 2p + d and p p' + 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 0 (1) length scale.

• 出版日期2017-8
• 单位MIT