[en] The most widely used charged as well as neutral particle transport solution method, the discrete-ordinates S_N, is plagued by slow convergence of the inner iteration process. This leads to unacceptable long computational times if it is applied to solve large problems, such as two-dimensional problems or where the self-scatter cross section approaches the value of the total cross section. Therefore, much effort was investigated to develop synthetic acceleration schemes. Synthetic acceleration schemes use a lower order equation with correction terms to make it consistent with the higher-order S_N-equation to be solved. The use of low-order S₂-equation, instead of diffusion, provides compatibility with any spatial discretization of the S_N transport equation and permits moments of higher than first order to be accelerated. In the present work low-order S_M scattering source correction scheme (S_M-SSCS) for two-dimensional geometry and finite elements in space is developed and investigated. The scheme was built into two-dimensional, x-y and r-z, triangular finite element S_N-transport code TRISM. We investigated the capability of the S₂-scattering source correction scheme calculating three benchmark problems and comparing the number of iterations and the computation time with values obtained using diffusion synthetic accelerated finite difference two-dimensional S_N transport code TWODANT. (author) 1 tab., 5 refs