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Finite Element Method with Applications in Engineering by T. L. Eldho, Y. M. Desai

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2.3 METHOD OF WEIGHTED RESIDUALS

The MWR is a very useful tool to approximate solutions to differential equations. Here the differential equation is considered directly rather than its variational forms. An approximate solution has some error with respect to the exact solution. Depending on the problem, error may be in the domain or on the boundary or in both. The objective of the method is to reduce the error. The procedure through which the error minimization is implemented is called the weighted residual technique.

When method of weighted residual is used, the concerned problem is represented by differential equation valid over the domain Ω with the prescribed boundary conditions on the boundary Г. Initially, a trial function is assumed as ...

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