Library of Congress Cataloging-in•Publication Data Brenner, Susanne C. The mathematical theory of finite element methods / Susanne C. Brenner, L. Ridgway Scott.-2nd ed. p. ; cm. -(Texts in applied mathematics; 15) Includes bibliographical references and index.
Abstract. In this paper, we propose a modified Lagrange type interpolation operator to approximate functions in Sobolev spaces by continuous piecewise polynomials. In order to define interpolators for "rough" functions and to preserve piecewise polynomial boundary conditions, the approximated functions are averaged appropriately either on d-or (d -1 )-simplices to generate nodal values for the interpolation operator. This combination of averaging and interpolation is shown to be a projection, and optimal error estimates are proved for the projection error.
Library of Congress Cataloging-in-Publication Data Brenner, Susanne C. The mathematical theory of finite element methods / Susanne C. Brenner, L. Ridgway Scott p. cm. -(Texts in applied mathematics j 15) Inc1udes bibliographical references and index.
Abstract. In this paper, we propose a modified Lagrange type interpolation operator to approximate functions in Sobolev spaces by continuous piecewise polynomials. In order to define interpolators for "rough" functions and to preserve piecewise polynomial boundary conditions, the approximated functions are averaged appropriately either on d-or (d -1 )-simplices to generate nodal values for the interpolation operator. This combination of averaging and interpolation is shown to be a projection, and optimal error estimates are proved for the projection error.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.