Research Article
Numerical Solution of the Heat Transfer Equation Coupled with the Darcy Flow Using the Finite Element Method
Table 1
Comparison of the exact and the numerical solutions using the finite element method for
, , and
.
| | | | Exact solution | FEM solution | Absolute error |
| | 0 | 0 | 0 | 0 | 0 | 1 | 0.3 | 0.3 | 0.4109 | 0.4143 | 0.0034 | | 0.6 | 0.6 | 0.6373 | 0.6498 | 0.0125 | | 1 | 1 | 0 | 0 | 0 | | 0 | 0 | 0 | 0 | 0 | 15 | 0.3 | 0.3 | 3.1357 | 3.5754 | 0.4398 | | 0.6 | 0.6 | 4.8634 | 5.6284 | 0.7651 | | 1 | 1 | 0 | 0 | 0 | | 0 | 0 | 0 | 0 | 0 | 50 | 0.3 | 0.3 | 9.9476 | 10.0780 | 0.1304 | | 0.6 | 0.6 | 15.4289 | 15.9524 | 0.5235 | | 1 | 1 | 0 | 0 | 0 | | 0 | 0 | 0 | 0 | 0 | 100 | 0.3 | 0.3 | 19.6789 | 18.8804 | 0.7985 | | 0.6 | 0.6 | 30.5223 | 30.0240 | 0.4984 | | 1 | 1 | 0 | 0 | 0 |
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