Header

UZH-Logo

Maintenance Infos

Construction of a p-adaptive continuous residual distribution scheme


Abgrall, Rémi; Viville, Q; Beaugendre, H; Dobrzynski, C (2017). Construction of a p-adaptive continuous residual distribution scheme. Journal of Scientific Computing, 72(3):1232-1268.

Abstract

A p-adaptive continuous residual distribution scheme is proposed in this paper. Under certain conditions, primarily the expression of the total residual on a given element K into residuals on the sub-elements of K and the use of a suitable combination of quadrature formulas, it is possible to change locally the degree of the polynomial approximation of the solution. The discrete solution can then be considered non continuous across the interface of elements of different orders, while the numerical scheme still verifies the hypothesis of the discrete Lax–Wendroff theorem which ensures its convergence to a correct weak solution. We detail the theoretical material and the construction of our p-adaptive method in the frame of a continuous residual distribution scheme. Different test cases for non-linear equations at different flow velocities demonstrate numerically the validity of the theoretical results. © 2017, Springer Science+Business Media New York.

Abstract

A p-adaptive continuous residual distribution scheme is proposed in this paper. Under certain conditions, primarily the expression of the total residual on a given element K into residuals on the sub-elements of K and the use of a suitable combination of quadrature formulas, it is possible to change locally the degree of the polynomial approximation of the solution. The discrete solution can then be considered non continuous across the interface of elements of different orders, while the numerical scheme still verifies the hypothesis of the discrete Lax–Wendroff theorem which ensures its convergence to a correct weak solution. We detail the theoretical material and the construction of our p-adaptive method in the frame of a continuous residual distribution scheme. Different test cases for non-linear equations at different flow velocities demonstrate numerically the validity of the theoretical results. © 2017, Springer Science+Business Media New York.

Statistics

Altmetrics

Downloads

0 downloads since deposited on 09 Oct 2017
0 downloads since 12 months

Additional indexing

Item Type:Journal Article, refereed, original work
Communities & Collections:07 Faculty of Science > Institute of Mathematics
Dewey Decimal Classification:510 Mathematics
Language:English
Date:1 September 2017
Deposited On:09 Oct 2017 16:42
Last Modified:09 Oct 2017 16:42
Publisher:Springer
ISSN:0885-7474
Publisher DOI:https://doi.org/10.1007/s10915-017-0399-6

Download

Content: Published Version
Language: English
Filetype: PDF - Registered users only
Size: 8MB
View at publisher