Symbolic-Numerical Algorithm for Generating Interpolation Multivariate Hermite Polynomials of High-Accuracy Finite Element Method

Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 10490)


A symbolic-numerical algorithm implemented in Maple for constructing Hermitian finite elements 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 across the boundaries of elements together with the derivatives up to a given order, which is used to solve elliptic boundary value problems using the high-accuracy finite element method. The efficiency and the accuracy order of the finite element scheme, algorithm and program are demonstrated by the example of the 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.


Hermite interpolation polynomials Boundary-value problem High-accuracy finite element method 


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© Springer International Publishing AG 2017

Authors and Affiliations

  1. 1.Joint Institute for Nuclear ResearchDubnaRussia
  2. 2.RUDN UniversityMoscowRussia
  3. 3.Institute of MathematicsNational University of MongoliaUlaanbaatarMongolia
  4. 4.N.G. Chernyshevsky Saratov National Research State UniversitySaratovRussia
  5. 5.Institute of PhysicsUniversity of M. Curie-SkłodowskaLublinPoland

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