The Reduced-Order Extrapolating Method about the Crank-Nicolson Finite Element Solution Coefficient Vectors for Parabolic Type Equation
Abstract
:1. Introduction
2. The CNFE Method for the Parabolic Type PDE
3. The ROECNFE Method for the Parabolic Type PDE
3.1. Generation of POD Bases
3.2. Formulation of Matrix-Form ROECNFE Model
3.3. The Stability and Error Estimates to the ROECNFE Solutions
4. Some Numerical Tests
5. Conclusions and Discussions
Funding
Conflicts of Interest
References
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CNFE Model | ROECNFE Matrix-Model | |||||
---|---|---|---|---|---|---|
t | n | CPU Run Time | CPU Run Time | |||
250 | 1.010356 × | 43.568 s | 4.050523 × | 1.623 s | ||
500 | 2.012083 × | 86.865 s | 4.350732 × | 2.265 s | ||
750 | 3.125338 × | 129.914 s | 4.671732 × | 2.873 s | ||
1000 | 1.015376 × | 172.931 s | 4.952762 × | 3.492 s | ||
1250 | 1.414376 × | 215.982 s | 5.251718 × | 4.013 s | ||
1500 | 2.534283 × | 259.173 s | 5.552123 × | 4.621 s | ||
1750 | 3.241232 × | 302.842 s | 5.856431 × | 5.276 s | ||
2000 | 2.562183 × | 345.874 s | 6.172762 × | 5.813 s |
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Luo, Z. The Reduced-Order Extrapolating Method about the Crank-Nicolson Finite Element Solution Coefficient Vectors for Parabolic Type Equation. Mathematics 2020, 8, 1261. https://doi.org/10.3390/math8081261
Luo Z. The Reduced-Order Extrapolating Method about the Crank-Nicolson Finite Element Solution Coefficient Vectors for Parabolic Type Equation. Mathematics. 2020; 8(8):1261. https://doi.org/10.3390/math8081261
Chicago/Turabian StyleLuo, Zhendong. 2020. "The Reduced-Order Extrapolating Method about the Crank-Nicolson Finite Element Solution Coefficient Vectors for Parabolic Type Equation" Mathematics 8, no. 8: 1261. https://doi.org/10.3390/math8081261