This paper presents a unifying framework for Trefftz-like methods, which allows the analysis and construction of discretization methods based on the decomposition into, and coupling of, local and global problems. We apply the framework to provide a comprehensive error analysis for the Embedded Trefftz discontinuous Galerkin method, for a wide range of second-order scalar elliptic partial differential equations and a scalar reaction-advection problem. We also analyze quasi-Trefftz methods with our framework and build bridges to other methods that are similar in virtue.

翻译：本文提出了Trefftz类方法的统一框架，该框架支持基于局部问题与全局问题分解及耦合的离散化方法的分析与构建。我们应用该框架对嵌入式Trefftz间断伽辽金方法进行了全面的误差分析，涵盖广泛的二阶标量椭圆型偏微分方程及标量反应-平流问题。同时，我们通过该框架分析了拟Trefftz方法，并建立了与具有相似特性的其他方法之间的理论桥梁。