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Table 1 Observed convergence rates in Figures 3 , 4 , 6 and 7 for uniform and adaptive mesh refining

From: A posteriori error analysis of stabilised FEM for degenerate convex minimisation problems under weak regularity assumptions

Example of subsection   σ- σ L p ( Ω ) 2 u- u L 2 ( Ω ) 2 η R η F η L D(u- u ) L 2 ( Ω ) 2 η H
   unstab. stab. unstab. stab. unstab. stab. stab. unstab. stab. stab.
  unif 5/3 5/3 3/2 7/5 4/5 4/5 1 3/5 1/2 1/3
‘Two-well benchmark’ R-adapt 2 7/5 (5/3) 6/5 1 1 1 (2/3) 2/5 2/5
  F-adapt 2 4/3 (5/3) 6/5 1 1 1 (2/3) 2/5 2/5
  unif 5/3 5/3 3/2 7/5 4/5 4/5 1 3/5 1/2 1/3
‘Modified two-well benchmark’ R-adapt 2 7/5 (5/3) 6/5 1 1 1 (2/3) 2/5 2/5
  F-adapt 11/5 4/3 (7/4) 6/5 1 1 1 (2/3) 2/5 2/5
  unif (1) 3/2 7/5 1 4/5 1 1/2 2/5
‘Three-well benchmark’ R-adapt 2 (1/4) (1/4) 1 (1/3) (1) (1/5)
  F-adapt 9/5 1 4/5 1 3/5 4/5 1/3 1/3
  unif      4/5 4/5 6/5    2/5
‘An optimal design example’ R-adapt      1 4/5 6/5    2/5
  F-adapt      1 4/5 1    2/5
  1. Convergence rates are given as powers of the representative mesh-size 1 / ndof which is proportional to H on uniform grids. Unavailable values are left blank, non-continuous rates are put in parantheses, inconclusive convergence behaviour is marked by “—”.