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It is shown in this paper that non-conforming finite elements on the triangleusing $P^{1}$-nonconforming polynomials and $P^{2}$ -conforming polynomials canbe easily built and used.They appear as an 'enriched' version of the standardpiecewise quadratic six-node element.This work is divided into two parts.In thefirst we present the basic- property of the element,namely how it can be builtand basic error estimates.We have observed that this new element behaves like$P^{1}$ non-conforming element.In the second part we have applied our elementto the elliptic problem and the theoretical estimate has been guaranteed bynumerical result.

Analysis of a combined NC1-C2 method for elliptic problem