TY - JOUR

T1 - Smoothness of Functions in Spaces of the Finite Element Method

AU - Dem’yanovich, Yu K.

AU - Prozorova, E. V.

N1 - Dem’yanovich, Y.K., Prozorova, E.V. Smoothness of Functions in Spaces of the Finite Element Method. J Math Sci 235, 262–274 (2018). https://doi.org/10.1007/s10958-018-4073-9

PY - 2018/12

Y1 - 2018/12

N2 - We find necessary and sufficient conditions for the generalized smoothness of the coordinate functions obtained from the approximate relations. We show that for the coordinate functions the smoothness on their supports is equivalent to that on the boundaries of supports. We obtain conditions for the continuity of Courant type finite element approximations and conditions for the uniqueness of a linear space of such approximations.

AB - We find necessary and sufficient conditions for the generalized smoothness of the coordinate functions obtained from the approximate relations. We show that for the coordinate functions the smoothness on their supports is equivalent to that on the boundaries of supports. We obtain conditions for the continuity of Courant type finite element approximations and conditions for the uniqueness of a linear space of such approximations.

UR - http://www.scopus.com/inward/record.url?scp=85054575437&partnerID=8YFLogxK

U2 - 10.1007/s10958-018-4073-9

DO - 10.1007/s10958-018-4073-9

M3 - Article

AN - SCOPUS:85054575437

VL - 235

SP - 262

EP - 274

JO - Journal of Mathematical Sciences

JF - Journal of Mathematical Sciences

SN - 1072-3374

IS - 3

ER -