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Order-preserving interpolation for summation-by-parts operators a t nonconforming grid interfaces

Journal article
Authors M. Almquist
Siyang Wang
J. Werpers
Published in SIAM Journal on Scientific Computing
Volume 41
Issue 2
ISSN 1064-8275
Publication year 2019
Published at Department of Mathematical Sciences
Language - English
Links doi.org/10.1137/18M1191609
Subject categories Mathematics

Abstract

- We study nonconforming grid interfaces for summation-by-parts finite difference methods applied to partial differential equations with second derivatives in space. To maintain energy stability, previous efforts have been forced to accept a reduction of the global convergence rate by one order, due to large truncation errors at the nonconforming interface. We avoid the order reduction by generalizing the interface treatment and introducing order-preserving interpolation operators. We prove that, given two diagonal-norm summation-by-parts schemes, order-preserving interpolation operators with the necessary properties are guaranteed to exist, regardless of the grid-point distributions along the interface. The new methods retain the stability and global accuracy properties of the underlying schemes for conforming interfaces. © 2019 Society for Industrial and Applied Mathematics

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