Nonlinearly-Stable High-Order Methods on Simplices with Improved Efficiency
David Zingg
DZ
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Summary (AI generated)
The Multidimensional SBP operator must accurately approximate derivatives. It should be decomposable using the SPD matrix. Additionally, it is essential that the relationship ( Q + Q^T = E ) holds, where ( E ) approximates the surface integral.
![Multidimensional SBP Property
1. Degree p accuracy conditions
DxPk=plk)
2. Px = H-1Qx = where H is symmetric positive definite
3. ex+ = where Ex satisfies
[1,2,...,n*] where T p
D is the derivative operator, H approximates a volume integral, and E approximates a surface integral](https://cassyni-user-files-prod.s3.amazonaws.com/5L73eyw8jC1hgQ4YR2gQcE)