The author's algebraic theory of boundary value problems has permitted systematizing Trefftz method and expanding its scope. The concept of TH-completeness has played a key role for such developments. This paper is devoted to revise the present state of these matters. Starting from the basic concepts of the algebraic theory, Green-Herrera formulas are presented and Localized Adjoint Method (LAM) derived. Then the classical Trefftz method is shown to be a particular case of LAM. This leads to a natural generalization of Trefftz method and a special class of domain decomposition methods: Trefftz-Herrera domain decomposition. © 1995.
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