Fig. 20: Comparison of envelope curves with the different subelement quadrature schemes with l/h = 1.0 and kφ = 0.002; centred crack: solid lines, shifted crack: dashed lines
 

Here, the upper values (envelope curves) of the point data of the numerical quadrature error e^int_Γlς (Eq. 58) of the crack surface integral (the max. expected error) with respect to the number of integration points is shown for quadrature stategies (1,2,3,4,6 GP per subelement). The phase-field is not numerically calculated by the means of FE but the stabilised phase-field is given (φς) as well as the analytical solution (φ). The solid lines refer to a given crack in the middle of the bar and the dashed lines refer to a given crack at a off-center position. 

for each file -> Columns
1: number of integration points 
2: error 

file fig_20_data_1.csv:  1 GP, centred crack (solid lines)
file fig_20_data_2.csv:  2 GP, centred crack (solid lines)
file fig_20_data_3.csv:  3 GP, centred crack (solid lines)
file fig_20_data_4.csv:  4 GP, centred crack (solid lines)
file fig_20_data_5.csv:  6 GP, centred crack (solid lines)

file fig_20_data_6.csv:  1 GP, shifted crack (dashed lines)
file fig_20_data_7.csv:  2 GP, shifted crack (dashed lines)
file fig_20_data_8.csv:  3 GP, shifted crack (dashed lines)
file fig_20_data_9.csv:  4 GP, shifted crack (dashed lines)
file fig_20_data_10.csv: 6 GP, shifted crack (dashed lines)