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arXiv · 2606.03845

Embedded Trefftz DG method for reaction-diffusion problems on anisotropic meshes

Sergio Gómez·Chiara Perinati·Paul Stocker·Igor Voulis
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Abstract

We present and analyze an embedded Trefftz discontinuous Galerkin method for reaction-diffusion problems on anisotropic meshes. The method is constructed by imposing a relaxed local Trefftz condition via an embedding into a tensor-product DG space, yielding a reduced global system while preserving the approximation properties of the underlying high-order discretization. We prove stability and quasi-optimality on anisotropic, possibly curved, quadrilateral elements, and derive anisotropic a priori error estimates. Numerical experiments for $h$- and $hp$-refinement, including curved-domain examples, validate the theoretical results.

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Sergio Gómez, Chiara Perinati, Paul Stocker, Igor Voulis. 2026-06-02. Embedded Trefftz DG method for reaction-diffusion problems on anisotropic meshes. https://arxiv.org/abs/2606.03845

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