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Table 3 The errors and convergence rates of \(\pmb{u-u^{hk}}\) in the \(\pmb{L^{2}(L^{2})}\) and \(\pmb{L^{2}(H^{1})}\) norms concerning  h

From: Convergence of a space-time continuous Galerkin method for the wave equation

h

Error in \(\boldsymbol{L^{2}(L^{2})}\)

Rate

Error in \(\boldsymbol{L^{2}(H^{1})}\)

Rate

1/8

6.4243e − 2

 

2.1045e − 0

 

1/16

1.6078e − 2

1.9985

1.0594e − 0

0.9902

1/32

4.0188e − 3

2.0003

5.3134e − 1

0.9956

1/64

9.8849e − 4

2.0235

2.6487e − 1

1.0043