An Adaptive Mesh Refinement for the Finite Element Method : (Trial by the r-Method)

Many automatic mesh generators for FEM are popularly in use, but in none of them is the finite element approximation error considered. This paper is concerned with an adaptive mesh refinement for FEM, in which the finite element approximation error is considered. In the analysis, the interpolation error gives the upper bound of the approximation errors. Here, we use interpolation error instead of approximation error. And we calculate the error measure; then, remesh is carried out by only relocating the nodes, without increasing the total number of nodes and elements. The method is applied to 3-node triangular elements and the stress analysis of linearly elastic structures. The γ-method is tested in two examples of stress analysis problems, and its effect is confirmed.