A non-conforming piecewise quadratic finite element on triangles

The employment of a piecewise quadratic element on the triangle for approximating second-order 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.