We introduce new nonconforming finite element methods for elliptic problems of second order. In contrast to previous work, we consider mixed boundard conditions and the domain does not have to lie on one side of its boundary. Each method is quasi-optimal in a piecewise energy norm, thanks to the discretization of the load functional with a moment-preserving smoothing operator.
Quasi-Optimal Nonconforming Methods for Second-Order Problems on Domains with Non-Lipschitz Boundary / A. Veeser, P. Zanotti (LECTURE NOTES IN COMPUTATIONAL SCIENCE AND ENGINEERING). - In: Numerical Mathematics and Advanced Applications ENUMATH 2017 / [a cura di] F. Radu, K. Kumar, I. Berre, J. Nordbotten, I. Pop. - Prima edizione. - [s.l] : Springer, Cham, 2019. - ISBN 9783319964140. - pp. 461-469 (( convegno ENUMATH 2017 tenutosi a Voss nel 2017 [10.1007/978-3-319-96415-7_41].
Quasi-Optimal Nonconforming Methods for Second-Order Problems on Domains with Non-Lipschitz Boundary
A. Veeser;P. Zanotti
2019
Abstract
We introduce new nonconforming finite element methods for elliptic problems of second order. In contrast to previous work, we consider mixed boundard conditions and the domain does not have to lie on one side of its boundary. Each method is quasi-optimal in a piecewise energy norm, thanks to the discretization of the load functional with a moment-preserving smoothing operator.
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