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Journal of Scientific Computing

Erschienen in:

13.03.2017

Construction of a p-Adaptive Continuous Residual Distribution Scheme

verfasst von: R. Abgrall, Q. Viville, H. Beaugendre, C. Dobrzynski

Erschienen in: Journal of Scientific Computing | Ausgabe 3/2017

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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.

Vorheriger Artikel Numerical Analysis of Fully Discretized Crank–Nicolson Scheme for Fractional-in-Space Allen–Cahn Equations

Nächster Artikel Linearized Conservative Finite Element Methods for the Nernst–Planck–Poisson Equations

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Titel: Construction of a p-Adaptive Continuous Residual Distribution Scheme
verfasst von: R. Abgrall
Q. Viville
H. Beaugendre
C. Dobrzynski
Publikationsdatum: 13.03.2017
Verlag: Springer US
Erschienen in: Journal of Scientific Computing / Ausgabe 3/2017
Print ISSN: 0885-7474
Elektronische ISSN: 1573-7691
DOI: https://doi.org/10.1007/s10915-017-0399-6

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