Introduction to direct variational and moment methods and an application to the Child-Langmuir law
Journal article, 2015

A short introduction is given of direct variational methods and its relation to Galerkin and moment methods, all flexible and powerful approaches for finding approximate solutions of difficult physical equations. A pedagogical application of moment methods is given to the physically and technically important Child–Langmuir law in electron physics. The analysis is shown to provide simple, yet accurate, approximate solutions of the two-dimensional problem (a problem which does not allow an exact analytical solution)and illustrates the usefulness and the power of moment methods.

direct variational methods

moment methods

Child–Langmuir law


Dan Anderson

Chalmers, Earth and Space Sciences, Plasma Physics and Fusion Energy

Mats Desaix

University of Borås

European Journal of Physics

0143-0807 (ISSN)

Vol. 2015 36 065032- 065032


Basic sciences

Learning and teaching

Pedagogical work

Subject Categories

Fusion, Plasma and Space Physics

Mathematical Analysis



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4/5/2022 6