
17Chapter two: General formulation of the discontinuous Galerkin method
Equation (2.34). The variable and coordinates can be interpolated within
an element by using Equation (2.35).
ξη=−ξ−η
ξη=ξ
ξη=η
(, )1
(, )
(, )
1
2
3
N
N
N
(2.34)
∑
∑
∑
η
η
η
=
=
=
(, )
(, )
ˆ
(, )
1
3
1
3
1
3
xNx
yNy
U
j
j
j
(2.35)
2.3.3 Integral calculation with isoparametric mapping
Using the isoparametric mapping, the integration can be performed by
the method of variable substitution, also called coordinate transforma-
tion. The mass matrix in 1D is given by Equation (2.36). The correspond-
ing mass matrix in the local coordinate is given by Equation (2.37). The
Jacobian ...