Two objectives have been formulated: to guarantee the invariance of algebraic analogues of integral-differential equations corresponding to the invariance of the original integral-differential equations system and to include boundary conditions directly into approximating dependences (shape functions) describing the field inside finite elements pertaining to the border. The above problem has been solved using the technique of invariant approximation of functions. As it has been shown, this approach reduces the order of the original system of equations.
- E. Süli, Finite Element Methods for Partial Differential Equations, University of Oxford. 2000.
- M. Zlámál, “On the Finite Element Method”, Numerische Mathematik, vol. 12, no. 5, pp. 394-402, 1968.
- G. Dziuk, C.M. Elliott, ”Surface Finite Elements for Parabolic Equations”, Journal of Computational Mathematics, vol. 25, no. 4, pp. 385-407, 2007.
- R. Filc “Discrete Analogy of the Hamilton’s Operator”, Mathematical Methods and Physical-Mechanics Fields, no. 24, 20-25, 1986. (Russian)