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  3. Volume 5, Number 1, 2018
  4. Finite element approximations in projection methods for solution of some Fredholm integral equation of the first kind

Finite element approximations in projection methods for solution of some Fredholm integral equation of the first kind

MMC.
2018;
Volume 5, Number 1
: pp. 74-87
https://doi.org/10.23939/mmc2018.01.074
Received: April 05, 2018

Math. Model. Comput. Vol. 5, No. 1, pp. 74-87 (2018)

Authors:
  1. O. Polishchuk
1
Pidstryhach Institute for Applied Problems of Mechanics and Mathematics National Academy of Sciences of Ukraine

Approximation properties of B-splines and Lagrangian finite elements in Hilbert spaces of functions defined on surfaces in three-dimensional space are investigated.  The conditions for the convergence of Galerkin and collocation methods for solution of the Fredholm integral equation of the first kind for the simple layer potential that is equivalent to the Dirichlet problem for Laplace equation in $\mathbb{R}^3$ are established.  The estimation of the error of approximate solution of this problem, obtained by means of the potential theory methods, is determined.

potential
integral equation
well-posed solvability
B-spline
Lagrange interpolation
Galerkin method
collocation method
convergence
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