A Unified Framework for Trefftz-like Discretization Methods
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Trefftz discontinuous Galerkin methods provide an efficient approach to discretizing partial differential equations (PDEs) by utilizing basis functions that satisfy the governing equation locally. In this talk, we introduce a unified framework for Trefftz-like discretization methods, which systematically decomposes the problem into local and global components. We apply this framework to provide a comprehensive error analysis for the Embedded Trefftz discontinuous Galerkin method, which avoids the explicit construction of Trefftz spaces by embedding them within a standard polynomial formulation. This enables the method to handle a broader range of PDEs, including those with non-constant coefficients or inhomogeneous terms, while ensuring computational efficiency. Our findings establish a robust theoretical foundation for extending Trefftz methods to more general PDE problems.