有限要素法における事後誤差評価とアダプティブメッシュ

抄録

This paper surveys some methods for a posteriori error estimation and their use in the adaptive remeshing for solving linear elasticity problems. A posteriori error estimates covered in this paper are: (i) the method of Zienkiewicz and Zhu based on the discontinuity of stress between elements, (ii) the method of Ohtsubo and Kitamura based on the residual of weak form of boundary value problem, (iii) the method of Oden et al. based on the residual and projection, and (iv) the method of Babuska and Rheinbolt based on the residual of subdomain. These methods are compared with respect to accuracy and computation time. They form a basis for the h-method, which is a method of adaptive remeshing of finite elements that aims at minimizing the total error norm using a given number of nodes in the finite element discretization. Several numerical examples are presented, such as plane stress problems, a plate bending problem, and a three dimensional elastic problem.