Bubble-Enriched Least-Squares Finite Element Method for Transient Advective Transport

Table 1

Convection of Gaussian hill by $t=0.6$.

	CN-LSFEM		ST-LSFEM		BE-LSFEM
Courant no.	$U_{\min \hspace{0.17em}}$	$U_{\max \hspace{0.17em}}$	$U_{\min \hspace{0.17em}}$	$U_{\max \hspace{0.17em}}$	$U_{\min \hspace{0.17em}}$	$U_{\max \hspace{0.17em}}$	%redn. in $U_{\min \hspace{0.17em}}$	%gain in $U_{\max \hspace{0.17em}}$
0.5	$-$0.0055	0.6861	$-$0.0186	0.6784	$-$ 0.0013^†	0.6967^†	76.9	1.55
1.0	$-$0.0490	0.6606	$-$0.1004	0.6196	$\approx 0$	0.7140	$\approx 100$	8.08
1.5	$-$0.1196	0.6210	$-$0.1536	0.5532	$-$0.1049	0.6401	12.2	3.1

^†with one bubble in both $x$ and $t$.