An Application of Richardson Extrapolation on FEM Solutions

AUTHOR(S):

TITLE

An Application of Richardson Extrapolation on FEM Solutions

ABSTRACT

The finite element metod (FEM) is widely used numerical method for numerical computation of different physical problems. The sequence of finite element method solutions with increasing the number of finite elements converge to analytical solutions. The idea for implementation of Richardson extrapolation is to get better solutions with less computation and without further increasing of number of finite elements what leads to larger systems of equations. The Richardson extrapolation is applied on finite element method solution in elastostatics. An algorithm for new solution calculated by Richardson method is given. The solutions calculated by applying Richardson extrapolation show more efficiency and accuracy with much less computation than solution with finite element method over more finite elements.

KEYWORDS

Richardson extrapolation, finite element method, elastostatics

REFERENCES

[1] J. L. Buchanan and P. A. Turner, Numerical Methods and Analysis, McGraw Hill, 1992 [1] J. L. Buchanan and P. A. Turner, Numerical Methods and Analysis, McGraw Hill, 1992

[2] C. O. E. Burg and T. Erwin, Application of Richardson extrapolation to the Numerical Solution of Partial Differential Equation, Numerical Methods for Partial Differential Equations, 25, 2009, pp. 810–832.

[3] M. Mestrovi ˇ c and E. Ocvirk, An application of ´ Romberg extrapolation on quadrature method for solving linear Volterra integral equations of the second kind, Applied Mathematics and Computation, 194, 2007, pp. 389–393.

Cite this paper

Mladen Mestrovic. (2016) An Application of Richardson Extrapolation on FEM Solutions. International Journal of Mathematical and Computational Methods, 1, 351-354