Towards a procedure to automatically improve finite element solutions by interpolation covers

• A scheme to improve finite element solutions by use of interpolation covers is presented.
• Low-order finite elements are considered.
• The scheme is developed to automatically improve finite element solutions.
• An error indicator is employed to automatically establish which order cover to apply.
• Some problems are solved to illustrate the procedure.

In a previous paper (Kim and Bathe, 2013) [1], we introduced a scheme to improve finite element displacement and stress solutions by the use of interpolation covers. In the present paper we show how the scheme can be used to automatically improve finite element solutions. As in Ref. (Kim and Bathe, 2013) [1], we focus on the use of the low-order finite elements for the analysis of solids, namely, the 3-node triangular and 4-node tetrahedral elements with the use of interpolation covers. An error indicator is employed to automatically establish which order cover to apply at the finite element mesh nodes to best improve the accuracy of the solution. Some two- and three-dimensional problems are solved to illustrate the procedure.