Order Preserving Interpolation for Summation-by-Parts Operators at Non-Conforming Grid Interfaces

Abstract

We study non-conforming 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 non-conforming 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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Cited by in corpus (5)

• Elastic wave propagation in anisotropic solids using energy-stable finite differences with weakly enforced boundary and interface conditions
• A Non-stiff Summation-By-Parts Finite Difference Method for the Scalar Wave Equation in Second Order Form: Characteristic Boundary Conditions and Nonlinear Interfaces
• Non-stiff narrow-stencil finite difference approximations of the Laplacian on curvilinear multiblock grids
• Stable and high-order accurate finite difference methods for the diffusive viscous wave equation
• Boundary and interface methods for energy stable finite difference discretizations of the dynamic beam equation