<abstract xmlns="http://www.w3.org/1999/xhtml"><p>In this paper, the high accuracy mass-conserved splitting domain decomposition method for solving the parabolic equations is proposed. In our scheme, the time extrapolation and local multi-point weighted average schemes are used to approximate the interface fluxes on interfaces of sub-domains, while the interior solutions are computed by one dimension high-order implicit schemes in sub-domains. The important feature is that the developed scheme keeps mass conservation and are of second-order convergent in time and fourth-order convergent in space. Numerical experiments confirm the convergence.</p></abstract>

In this paper, the high accuracy mass-conserved splitting domain decomposition method for solving the parabolic equations is proposed. In our scheme, the time extrapolation and local multi-point weighted average schemes are used to approximate the interface fluxes on interfaces of sub-domains, while the interior solutions are computed by one dimension high-order implicit schemes in sub-domains. The important feature is that the developed scheme keeps mass conservation and are of second-order convergent in time and fourth-order convergent in space. Numerical experiments confirm the convergence.

The high accuracy conserved splitting domain decomposition scheme for solving the
parabolic equations

Applied Mathematics and Nonlinear Sciences

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.

In this paper, the high accuracy mass-conserved splitting domain decomposition method for solving the parabolic equations is proposed. In our scheme, the time...

r ∖ m		2	3	5	10	20
2	e_h	4.2699E+19	3.2818E+02	1.5482E-6	1.6600E-8	2.5564E-7
2	MassErr	1.4909E+02	6.2177E-16	8.2406E-18	9.7145E-19	2.0761E-17

τ ∖ D		0.01	0.1	0.5	1
1/1000	e_h	1.7193E-7	3.1160E-7	2.7226E-7	2.7227E-7
1/1000	MassErr	2.9837E-18	1.1241E-17	4.0246E-18	4.2986E-17

1/2000	e_h	1.7211E-7	3.0987E-7	3.1648E-7	1.4113E-7
1/2000	MassErr	3.7401E-17	2.6368E-17	2.3835E-17	4.1113E-18

1/3000	e_h	1.7218E-7	3.0962E-7	3.2929E-17	1.8791E-7
1/3000	MassErr	3.1850E-17	4.4409E-17	4.4548E-17	6.9042E-18

1/4000	e_h	1.7221-7	3.0956E-7	3.3409E-7	2.0642E-7
1/4000	MassErr	4.8503-17	1.1796E-18	2.4876E-17	1.7781E-17

D ∖ τ		1/1000	1/4000	1/9000	1/16000
1E-2	e_h	3.3475E-5	1.6835E-5	1.1157E-5	8.3407E-6
1E-2	ratio	-	1.9695	2.2111	2.3563

1E-1	e_h	4.6382E-5	1.7548E-6	2.5642E-7	6.7091E-8
1E-1	ratio	-	2.3621	2.3717	2.3303

1	e_h	4.2394E-5	1.7795E-6	2.9232E-7	8.3107E-8
1	ratio	-	2.2872	2.2273	2.1860

D ∖ h		1/10	1/20	1/40	1/80
1E-2	e_h	1.0572E-5	6.8466E-7	2.9351E-8	9.9707E-10
1E-2	ratio	-	3.9487	4.5439	4.8796

1E-1	e_h	4.6522E-5	1.7552E-6	6.7088E-8	2.9600E-9
1E-1	ratio	-	4.7282	4.7094	4.5024

1	e_h	4.2444E-5	1.7928E-6	8.0280E-8	1.5923E-9
1	ratio	-	4.5653	4.4810	5.6559

The high accuracy conserved splitting domain decomposition scheme for solving the parabolic equations

Published Online: Dec 31, 2018

Page range: 583 - 592

Received: Oct 08, 2018

Accepted: Dec 31, 2018

DOI: https://doi.org/10.2478/AMNS.2018.2.00045

Keywords
Parabolic equations, time second-order, space fourth-order, mass-conserved, domain decomposition

© 2018 Z. Zhou and L. Li, published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.

Fig. 1

Fig. 2

The effect of m on the stability.

Errors and mass errors for different diffusion D and different τ.

Errors and ratios of convergence in time for different diffusion D.

Errors and ratios of convergence in space for different diffusion D.

The high accuracy conserved splitting domain decomposition scheme for solving the parabolic equations

Published Online: Dec 31, 2018

Page range: 583 - 592

Received: Oct 08, 2018

Accepted: Dec 31, 2018

DOI: https://doi.org/10.2478/AMNS.2018.2.00045

KeywordsParabolic equations, time second-order, space fourth-order, mass-conserved, domain decomposition

© 2018 Z. Zhou and L. Li, published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.

Fig. 1

Fig. 2

The effect of m on the stability.

Errors and mass errors for different diffusion D and different τ.

Errors and ratios of convergence in time for different diffusion D.

Errors and ratios of convergence in space for different diffusion D.

Keywords
Parabolic equations, time second-order, space fourth-order, mass-conserved, domain decomposition