A new 3D finite element for adaptive <i>h</i>‐refinement in 1‐irregular meshes

Abstract

Abstract A new finite element, viable for use in the three‐dimensional simulation of transient physical processes with sharply varying solutions, is presented. The element is intended to function in adaptive h ‐refinement schemes as a versatile transition between regions of different refinement levels, ensuring interelement continuity by constructing a piecewise linear solution at the element boundaries, and retaining all degrees of freedom in the solution phase. Construction of the element shape functions is described, and a numerical example is presented which illustrates the advantages of using such an element in an adaptive refinement problem. The new element can be used in moving‐front problems, such as those found in reservoir engineering and groundwater flow applications.