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.

Ämnesord

NATURVETENSKAP  -- Matematik (hsv//swe)

NATURAL SCIENCES  -- Mathematics (hsv//eng)

Nyckelord

summation-by-parts

nonconforming interfaces

interpolation

accuracy

finite-difference approximations

schemes

convergence

equation

Mathematics

rand b

1994

journal of computational physics

v110

p47

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