PROPOSAL FOR A NEW DISCRETE METHOD BASED ON AN ASSESSMENT OF DISCRETIZATION ERRORS
- 1 October 1980
- journal article
- research article
- Published by Taylor & Francis in Numerical Heat Transfer
- Vol. 3 (4) , 411-428
- https://doi.org/10.1080/01495728008961768
Abstract
Finite-difference and finite-element methods are widely used to solve problems described by sets of partial differential equations. However, the connections between the approximations made in the discretization process and the final solution errors, for a given grid, are often not clearly understood, especially when convection is a dominant factor. These connections are clarified in the present paper and, from the insight gained, a new method of formulating the discrete equations suggests itself. The results of applying two different schemes, that are both based on this method, to an example problem are presented. These are compared with results obtained using two finite-difference schemes. The new approach appears to hold considerable promise for future development.Keywords
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