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 ${𝒯}_h$ consisting of triangles and convex quadrilaterals is described and its accuracy is illustrated numerically. The method assumes that the interpolant ${\Pi }_h\left(u\right)$ in the finite element space of the linear triangular and bilinear quadrilateral finite elements from ${𝒯}_h$ is known only.

EUDML-ID : urn:eudml:doc:271375
Mots clés:
Mots clés:

@article{702707,
     title = {Superapproximation of the partial derivatives in the space of linear triangular and bilinear quadrilateral finite elements},
     booktitle = {Programs and Algorithms of Numerical Mathematics},
     series = {GDML\_Books},
     publisher = {Institute of Mathematics AS CR},
     address = {Prague},
     year = {2013},
     pages = {57-62},
     url = {http://dml.mathdoc.fr/item/702707}
}

Dalík, Josef. Superapproximation of the partial derivatives in the space of linear triangular and bilinear quadrilateral finite elements, dans Programs and Algorithms of Numerical Mathematics, GDML_Books,  (2013), pp. 57-62. http://gdmltest.u-ga.fr/item/702707/