Nonlinearly-Stable High-Order Methods on Simplices with Improved Efficiency - presented by David Zingg

Nonlinearly-Stable High-Order Methods on Simplices with Improved Efficiency

David Zingg

DZ

Slide at 08:34

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Linear Stability - Semi-Discrete Form
Summation-by-Parts Property
D = H-1Q
+QT =E =
+ aH-1Qu= = 0
TH du = -auTQu
=-a(uz-uz)
With a SAT to
enforce the boundary
Consistent with
continuous
condition (a > 0):
result

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Summary (AI generated)

Introducing a Strongly Admissible Technique (SAT) to enforce the boundary condition preserves the boundedness and stability observed in the continuous solution.