A new 3D finite element for adaptive h‐refinement in 1‐irregular meshes

Abstract

SUMMARYA 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.

21-node hexahedral isoparametric element for analysis of contact problems

“…with the entries of the elasto±plastic constitutive matrix D ep c given explicitly in Reference 13; a and b are explained by equation (3). It is pointed out that in the case of friction the system matrix is non-symmetric.…”

“…c is an elastic±plastic constitutive matrix obtained for a non-associated hardening friction model analogous to the classical theory of plasticity (for details we refer the reader to the author's Reference 13), t is the vector of contact tractions and det j is the determinant of the transformation Jacobian matrix given by equation (3). The superscript T indicates the matrix transpose.…”

A unified mesh refinement method with applications to porous media flow

“…the use of separate constraint equations rather than transition elements [9,10], are influenced by the object-oriented design and the corresponding possibility to incorporate the new Grid2FE in existing simulators without modification of already debugged implementation of the weak forms of the partial differential equations.…”

“…According to Morton et al, this approach is easier to integrate into an existing finite element code compared with methods based on separate constraint equations. However, the disadvantage with special transition elements [9,10] is that these new elements must be incorporated into the finite element library of a code, and the grid must then be composed of different element types. The present approach allows the original, standard element type and a standard, often highly optimized, finite element solver to be used.…”

“…Their paper is referred to for further discussion of previous work. Morton et al [9] presented a 3D algorithm in which the constraints associated with irregular nodes are incorporated by modifying the finite element basis functions, i.e. they introduce a family of new transition elements.…”