P-version of the finite element

Mesh refinement - h- and p-versions of the finite element method... 

The family of hierarchical elements are specifically designed to minimize the computational cost of repeated computations in the p-version of the finite element method (Zienkiewicz and Taylor, 1994). Successive approximations based on hierarchical elements utilize the derivations of a lower step to generate the solution for a higher-order approximation. This can significantly reduce the... 

There exist methods that are fully numerical, e.g., the finite element method [33,51], the DFT method [52], and the Monte Carlo method [53]. As mentioned above, the CHA problem was approached through the finite element method by Friedman et al. [33]. Recently Guimaraes and Prudente [51] used a variational procedure that is based on the p-version of the finite element method. Their results are very close to the most accurate values published to date [34,39,43]. In addition, through this method it is possible to analyze all states. 

PTC, Suggested Technique for Understanding the P-Version of the Finite Element Method, PTC Knowledge Database, http //ww w.ntc.com/. 

U-V-P schemes belong to the general category of mixed finite element techniques (Zienkiewicz and Taylor, 1994). In these techniques both velocity and pressure in the governing equations of incompressible flow are regarded as primitive variables and are discretized as unknowns. The method is named after its most commonly used two-dimensional Cartesian version in which U, V and P represent velocity components and pressure, respectively. To describe this scheme we consider the governing equations of incompressible non-Newtonian flow (Equations (1.1) and (1.4), Chapter 1) expressed as... 

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