Symbolic-Numerical Algorithms for Solving the Parametric Self-adjoint 2D Elliptic Boundary-Value Problem Using High-Accuracy Finite Element Method
نویسندگان
چکیده
Algorithms for Solving the Parametric Self-Adjoint 2D Elliptic Boundary-Value Problem Using High-Accuracy Finite Element Method A. A. Gusev*, O. Chuluunbaatar*†, S. I. Vinitsky*‡, V. L. DerbovS, A. Góźdź¶ * Joint Institute for Nuclear Research 6, Joliot-Curie, Dubna, Moscow region, Russia, 141980 † Institute of Mathematics, National University of Mongolia, Ulaanbaatar, Mongolia ‡ RUDN University (Peoples’ Friendship University of Russia) 6, Miklukho-Maklaya str., Moscow, Russia, 117198 S Saratov State University, Saratov, Russia ¶ Institute of Physics, University of M. Curie-Sk lodowska, Lublin, Poland
منابع مشابه
B-Spline Finite Element Method for Solving Linear System of Second-Order Boundary Value Problems
In this paper, we solve a linear system of second-order boundary value problems by using the quadratic B-spline nite el- ement method (FEM). The performance of the method is tested on one model problem. Comparisons are made with both the analyti- cal solution and some recent results.The obtained numerical results show that the method is ecient.
متن کاملSymbolic-Numerical Solution of Boundary-Value Problems with Self-adjoint Second-Order Differential Equation Using the Finite Element Method with Interpolation Hermite Polynomials
We present a symbolic algorithm generating finite-element schemes with interpolating Hermite polynomials intended for solving the boundary-value problems with self-adjoint second-order differential equation and implemented in the Maple computer algebra system. Recurrence relations for the calculation in analytical form of the interpolating Hermite polynomials with nodes of arbitrary multiplicit...
متن کاملOn Approximate Stationary Radial Solutions for a Class of Boundary Value Problems Arising in Epitaxial Growth Theory
In this paper, we consider a non-self-adjoint, singular, nonlinear fourth order boundary value problem which arises in the theory of epitaxial growth. It is possible to reduce the fourth order equation to a singular boundary value problem of second order given by w''-1/r w'=w^2/(2r^2 )+1/2 λ r^2. The problem depends on the parameter λ and admits multiple solutions. Therefore, it is difficult to...
متن کاملModified Fixed Grid Finite Element Method in the Analysis of 2D Linear Elastic Problems
In this paper, a modification on the fixed grid finite element method is presented and used in the solution of 2D linear elastic problems. This method uses non-boundary-fitted meshes for the numerical solution of partial differential equations. Special techniques are required to apply boundary conditions on the intersection of domain boundaries and non-boundary-fitted elements. Hence, a new met...
متن کاملModified Fixed Grid Finite Element Method in the Analysis of 2D Linear Elastic Problems
In this paper, a modification on the fixed grid finite element method is presented and used in the solution of 2D linear elastic problems. This method uses non-boundary-fitted meshes for the numerical solution of partial differential equations. Special techniques are required to apply boundary conditions on the intersection of domain boundaries and non-boundary-fitted elements. Hence, a new met...
متن کامل