### 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)