Stable lifting of polynomial traces on triangles
We construct a right inverse of the trace operator u 7→ (u|∂T , ∂nu|∂T ) on the reference triangle T that maps suitable piecewise polynomial data on ∂T into polynomials of the same degree and is bounded in all Ws,q (T) norms with 1 < q < ∞ and s ≥ 2. The analysis relies on new stability estima...
| Main Authors: | , |
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| Format: | Journal article |
| Language: | English |
| Published: |
Society for Industrial and Applied Mathematics
2024
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| Summary: | We construct a right inverse of the trace operator u 7→ (u|∂T , ∂nu|∂T ) on the reference triangle T that maps suitable piecewise polynomial data on ∂T into polynomials of the same degree and is bounded in all Ws,q (T) norms with 1 < q < ∞ and s ≥ 2. The analysis relies on new stability estimates for three classes of single edge operators. We then generalize the construction for mth-order normal derivatives, m ∈ N0. |
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