The procedure of this kind is capable of including a number of element refinements (addition of shear deformation, variable cross-section, etc).
The article entitled "Distributed Gram-Schmidt Orthogonalization with Simultaneous Elements Refinement", by O. Sluciak, H. Strakova, M. Rupp, and W. Gansterer, describes a distributed adaptive solution for the problem of Gram-Schmidt orthogonalization.
Numerical simulations of an air saturated polyurethane foam material show faster convergence for the hierarchical extensions than for linear and quadratic serendipity finite element mesh refinement extensions.
In the hp-version adaptation, one has the option to split an element (h-refinement) or to increase its approximation order (p-refinement).
An object-oriented geophysical and astrophysical spectral-element adaptive refinement (GASpAR) code is introduced.
Utilization of an appropriate dilution ratio and control of minor alloying elements, grain refinement and magnetic arc oscillations can minimise its occurrence.
Given the current adapted mesh, a criterion for selecting candidate elements for refinement and coarsening is adopted based on the locally largest value of the density gradient.
The new feature of the proposed method is the introduction of element-wise refinement switching between longest side bisection and octasection, to boost the quality improvement process of face swapping and node relaxation.
By means of this property, it is shown that the Dörfler marking strategy used to single out the elements for refinement, is not only sufficient for linear convergence (1.3), but in some sense even necessary.
He implicitly introduced the concept of separate Dörfler marking: If the data oscillations osc (T ℓ ; U (T ℓ ) ) are small compared to the error estimator η (T ℓ ; U (T ℓ ) ), he used the common Dörfler marking (2.5) to single out the elements for refinement.
