The weak problems of the fourth non-mixed boundary value problems of electrostatic fields. (Chinese. English summary) Zbl 0784.65093
Summary: We apply the finite element method to the fourth non-mixed boundary value problem of the electrostatic field (in the sense of Galerkin). By changing the boundary value problem to an equivalent problem we give the conditions to guarantee the uniqueness of the weak solution (up to constants) to the fourth non-mixed boundary value problems. We also discuss the formation of the coefficient matrix and the right-hand vector of the corresponding algebraic equations and give an example to demonstrate our method.
MSC:
65Z05 | Applications to the sciences |
65N30 | Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs |
35Q60 | PDEs in connection with optics and electromagnetic theory |
78A30 | Electro- and magnetostatics |