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arXiv · 2606.13229

Embedded Trefftz DG method for steady Navier-Stokes flow. Part I: Oseen linearization

Paul Stocker·Igor Voulis·Christoph Lehrenfeld·Philip L. Lederer
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Abstract

We develop an embedded Trefftz-DG method for the Oseen problem and prove a complete stability and quasi-optimality theory in standard DG norms. The key ingredient is a construction of a suitable local complement space to the Trefftz space, on which the Oseen operator is stably invertible. We also derive a reduced formulation of the method, the resulting system is posed in terms of the velocity unknown only, a crucial step in the analysis especially for the nonlinear Navier-Stokes problem in Part II.

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Paul Stocker, Igor Voulis, Christoph Lehrenfeld, Philip L. Lederer. 2026-06-11. Embedded Trefftz DG method for steady Navier-Stokes flow. Part I: Oseen linearization. https://arxiv.org/abs/2606.13229

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