Research Article
Numerical Solution of the Heat Transfer Equation Coupled with the Darcy Flow Using the Finite Element Method
Table 2
Comparison of the exact and the numerical solutions using the finite element method for
, , and
.
| | | | FE solution | Exact solution | Absolute error |
| | 0 | 0 | 2.0000 | 2.0000 | 0 | 1 | 0.3 | 0.3 | 2.0544 | 2.0000 | 0.0544 | | 0.6 | 0.6 | 2.0682 | 2.0000 | 0.0682 | | 1 | 1 | 2.0000 | 2.0000 | 0 | | 0 | 0 | 16.0000 | 16.0000 | 0 | 15 | 0.3 | 0.3 | 16.0544 | 16.0000 | 0.0544 | | 0.6 | 0.6 | 16.0682 | 16.0000 | 0.0682 | | 1 | 1 | 16.0000 | 16.0000 | 0 | | 0 | 0 | 51.0000 | 51.0000 | 0 | 50 | 0.3 | 0.3 | 51.0544 | 51.0000 | 0.0544 | | 0.6 | 0.6 | 51.0682 | 51.0000 | 0.0682 | | 1 | 1 | 51.0000 | 51.0000 | 0 | | 0 | 0 | 101.0000 | 101.0000 | 0 | 100 | 0.3 | 0.3 | 101.0544 | 101.0000 | 0.0544 | | 0.6 | 0.6 | 101.0682 | 101.0000 | 0.0682 | | 1 | 1 | 101.0000 | 101.0000 | 0 |
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