A Third Order Accurate Cellwise Relaxation Implicit Discontinuous Galerkin Scheme for Unstructured Hybrid Meshes

Table 1

Computed results for the parabolic equation using 2nd, 3rd, and 4th order schemes.

	Cell aspect ratio is 1			Cell aspect ratio is 1000
	Mesh-1a	Mesh-1b	Mesh-1c	Mesh-2a	Mesh-2b	Mesh-2c
Time steps needed for machine zero convergence
2nd order	3210	12320	46890	6110	22880	86260
3rd order	5990	22680	85880	11800	44650	168060
4th order	9430	35650	134830	17270	65340	247390
CPU time per one time step
2nd order	0.0099 [s]	0.0527 [s]	0.3961 [s]	0.0104 [s]	0.0528 [s]	0.4005 [s]
3rd order	0.0361 [s]	0.2212 [s]	1.8564 [s]	0.0359 [s]	0.2256 [s]	1.8497 [s]
4th order	0.1989 [s]	1.3447 [s]	10.520 [s]	0.1962 [s]	1.3376 [s]	10.482 [s]
Log10(Error) of converged solutions
2nd order	−2.5600	−4.8282	−6.2279	−2.7419	−4.7185	−7.0051
3rd order	−3.1516	−5.7300	−7.3960	−3.3393	−5.5940	−8.2653
4th order	−3.7487	−6.6345	−8.5852	−3.9279	−6.4839	−9.5030
Attained spatial accuracy
2nd order	1.96979			1.97443
3rd order	2.93233			3.00013
4th order	4.14892			3.91538