A nonconforming piecewise quadratic finite element on triangles
Abstract
The employment of a piecewise quadratic element on the triangle for approximating secondorder problems is investigated. It is shown that the triangular elements are quadratic elements which are enhanced by a shape function on each triangle and, subsequently, that nonconforming piecewise elements can be simply implemented. The shape function produces an interior node, which increases the computational complexity slightly. Consideration is given to error estimates and regularity properties for Direchlet's problem. Examples are provided in terms of applications to incompressible viscous flow, a potential flow between turbine blades, and a square cavity flow.
 Publication:

International Journal for Numerical Methods in Engineering
 Pub Date:
 April 1983
 DOI:
 10.1002/nme.1620190405
 Bibcode:
 1983IJNME..19..505F
 Keywords:

 Approximation;
 Finite Element Method;
 Quadratic Equations;
 Stokes Flow;
 Triangles;
 Viscous Flow;
 Cavity Flow;
 Computational Fluid Dynamics;
 Dirichlet Problem;
 Error Analysis;
 Flow Geometry;
 Potential Flow;
 Turbine Blades;
 Fluid Mechanics and Heat Transfer