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

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.

Wang, Siyang,1987Gothenburg University,Göteborgs universitet,Institutionen för matematiska vetenskaper,Department of Mathematical Sciences,Chalmers University of Technology, Sweden,MAM(Swepub:uu)siywa338 (författare)
Werpers, JonatanUppsala universitet,Avdelningen för beräkningsvetenskap,Numerisk analys(Swepub:uu)jonwe904 (författare)
Stanford UniversityStanford University, US (creator_code:org_t)

Ingår i:SIAM Journal of Scientific Computing: Society for Industrial and Applied Mathematics Publications41:2, s. A1201-A12271064-82751095-7197

Av författaren/redakt...: Almquist, Martin; Wang, Siyang, 19 ...; Werpers, Jonatan

Om ämnet

Av lärosätet: Chalmers tekniska högskola; Göteborgs universitet; Mälardalens universitet; Uppsala universitet

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