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.