Speaker
Dr
Alexander Gusev
(Laboratory of Information Technologies Joint Institute for Nuclear Research)
Description
High-accuracy finite element method for elliptic boundary-value problems is presented.
The basis functions of finite elements are high-order polynomials, determined from a specially constructed set of values of the polynomials themselves, their partial derivatives, and their derivatives along the directions of the normals to the boundaries of finite elements.
Such a choice of the polynomials allows us to construct a piecewise polynomial basis continuous on the boundaries of elements together with the derivatives up to a given order. In present talk we show how this basis is applied to solve elliptic boundary value problems in the limited domain of multidimensional Euclidean space, specified as a polyhedron.
The efficiency and the accuracy order of the finite element scheme, algorithm and program are demonstrated by the example of exactly solvable boundary-value problem for a triangular membrane, depending on the number of finite elements of the partition of the domain and the number of piecewise polynomial basis functions.
Primary author
Dr
Alexander Gusev
(Laboratory of Information Technologies Joint Institute for Nuclear Research)
Co-authors
Dr
Ochbadrakh Chuluunbaatar
(LIT JINR)
Prof.
Sergue Vinitsky
(BLTP JINR)
Prof.
Vladimir Gerdt
(Joint Institute for Nuclear Research)
