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In this paper, four three-node triangular finite element models which can readily be incorporated into the standard finite element program framework are devised via a multi-field variational functional for the bounded plane Helmholtz problem. In the models, boundary and domain fields are independently assumed. The former is constructed by nodal interpolation and the latter comprises nonsingular solutions of the Helmholtz equation. The equality of the two fields are enforced along the element boundary. Among the four devised models, the most accurate one is 1/3 to 1/2 less erroneous than the conventional single-field model in most examples. [ABSTRACT FROM AUTHOR]