${\mathsf{\Omega }}_r$	The domain of refined mesh.	${\mathsf{\Omega }}_{r1}, {\mathsf{\Omega }}_{r2}, \dots$	The domains of refined meshes in first, second levels, and so on.
${\mathsf{\Omega }}_c$	The domain of original coarse mesh.
$l_e$	The length of element edge.	${\mathit{u}}_1, {\mathit{u}}_2, \dots$	The displacements of node 1, node 2, and so on.
a	Half of the crack length.
L	Length of the plate.	N1, N2, …	Node 1, node 2, and so on.
B	Width of the plate.	${\sigma }_{xx}, {\sigma }_{yy}$	Normal stress in x and y directions.
t	Thickness of the plate
$r$	The distance from crack tip.	${\tau }_{xy}$	Shear stress in xy-plane.
${\sigma }_{\infty }$	Far-field stress.	$K_I, K_{II}$	Stress intensity factor of mode I, II loading.
$\theta$	The angle of crack in polar coordinates.
β	The angle of crack on the plate.	$\eta$	The ratio of the distance to crack tip and half of the crack length.
FEM	Finite element method
XFEM	Extended finite element method
LEFM	Linear elastic fracture mechanics
h-AES	h-adaptive element splitting