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Method of R-functions in problems with natural boundary conditions. (Russian) Zbl 0672.65103

Solutions are compared of two model problems of electrostatics obtained by means of general and partial structures, i.e., satisfying or not satisfying natural boundary conditions. The problem is solved for composite piecewise-homogeneous media with natural boundary conditions, also in the case of very different physical characteristics. In this case splines are used as basis functions. The analysis of the results obtained shows that taking into account only main boundary conditions in the theory of R-functions allows one to obtain sufficiently accurate solutions and at the same time to reduce the computer time needed.
Reviewer: O.Dumbrajs

MSC:

65Z05 Applications to the sciences
65N30 Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs
78A30 Electro- and magnetostatics
35Q99 Partial differential equations of mathematical physics and other areas of application
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