The spectral overlay on finite elements for problems with high gradients

A methodology has been developed for enhancing the accuracy of finite element solutions of problems with high gradients. This is accomplished by superimposing the spectral approximation on subdomains which overlay the finite element mesh in regions where high gradients are indicated by the solution. The orientation and shape of these subdomains are quite arbitrary. Results are obtained for a viscoplastic bar which is stretched beyond its bifurcation point. The results show that with a modest increase in the number of spectral unknowns, it is possible to achieve high resolution of the strain field in the shear band.