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

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7.5 FINITE ELEMENT SOLUTION OF PARTIAL DIFFERENTIAL EQUATIONS BY METHOD OF WEIGHTED RESIDUAL

In this section, the finite element formulations of some important steady-state partial differential equations governing the field problems in two dimensions are presented. In particular, Laplace equation, Poisson equation and Helmholtz equation are considered. Laplace equation is an elliptic equation used to characterize steady-state systems (Chapra and Canale, 2002). Thus, the two-dimensional form of Laplace equation can be used to determine the steady-state distribution of an unknown function in two spatial dimensions.

The Laplace equation can be used to model a variety of engineering problems involving potential of an unknown such as heat conduction ...

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