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ORDER-PRESERVING INTERPOLATION FOR SUMMATION-BY-PARTS OPERATORS AT NONCONFORMING GRID INTERFACES

Journal article
Authors M. Almquist
Siyang Wang
J. Werpers
Journal Of Computational Physics V. P. Rpenter Mh
Published in Siam Journal on Scientific Computing
Volume 41
Issue 2
Pages A1201-A1227
ISSN 1064-8275
Publication year 2019
Published at Department of Mathematical Sciences
Pages A1201-A1227
Language en
Links dx.doi.org/10.1137/18m1191609
Keywords summation-by-parts, nonconforming interfaces, interpolation, accuracy, finite-difference approximations, schemes, convergence, equation, Mathematics, rand b, 1994, journal of computational physics, v110, p47
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.

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