Adaptive Techniques in the Finite Element Method

Abstract

In computational methods, particularly the FEM, the adaptive refinement indicates an automatic convergence process. The motivations of adaptive study for hydraulic structures elucidated in this chapter are multi-fold inclusive pre-process facilitation and software standardization, of which the latter is more attractive because it may enable engineers to control the computation error tolerance for different grades of hydraulic structures, in lieu of optional and ambiguous consideration and discussion on the adequate mesh size. Towards this target, the most prevalent adaptive refinement schemes, namely, the h-version to control the error of approximation by means of element size and the p-version to control the error of approximation through the polynomial shape functions, are elaborated in this chapter. To be more practical for hydraulic structures, the issues of viscoplastic deformation, phreatic surface, refinement strategy, equation solver, etc., are specifically handled. This chapter is closed with a variety of validation examples (underground cavern, embankment dam, concrete dam, sluice) and two engineering application cases (cut slope, landslide).