Abstract

This chapter is focused to study situations governed by the general quasi-harmonic equation, the particular cases of which are the well-known Laplace and Poisson equations. The range of physical problems falling into this category is large, including heat conduction, seepage through porous media, irrotational flow of ideal fluids, and distribution of electrical potential. The formulation developed in this chapter is equally applicable to all. In all the above classes of problems, the behavior can be represented in terms of a scalar variable. Weak form and variational principle are applicable to the Poisson and Laplace equations. This chapter applies those approaches to a general, quasi-harmonic equation and indicates the ranges of applicability of a single as well as unified approach by which one computer program can solve a large variety of physical problems.

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