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Article

Dalík, Josef
Superapproximation of the partial derivatives in the space of linear triangular and bilinear quadrilateral finite elements. (English). In: Chleboun, J., Segeth, K., Šístek, J. and Vejchodský, T. (eds.): Programs and Algorithms of Numerical Mathematics. Proceedings of Seminar. Dolní Maxov, June 3-8, 2012. Institute of Mathematics AS CR, Prague, 2013. pp. 57-62
MSC: 65N30
Keywords:
superconvergence; finite element method
Summary:
A method for the second-order approximation of the values of partial derivatives of an arbitrary smooth function $u=u(x_1,x_2)$ in the vertices of a conformal and nonobtuse regular triangulation $\mathcal T_h$ consisting of triangles and convex quadrilaterals is described and its accuracy is illustrated numerically. The method assumes that the interpolant $\Pi_h(u)$ in the finite element space of the linear triangular and bilinear quadrilateral finite elements from $\mathcal T_h$ is known only.
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