In　this　paper,　a　finite　element　method　for　general　scalar　conservation　laws　is　analyzed:　convergence　towards　the　unique　solution　is　proved　for　two-dimensional　space　with　initial　and　boundary　conditions,　by　using　a　uniqueness　theorem　for　measure　valued　solutions.　The　method　has　some　advantages:　it　is　an　explicit　finite　element　scheme,　which　is　suitable　for　computing　convection　dominated　flows　and　discontinuous　solutions　for　multi-dimensional　hyperbolic　conservation　laws.　It　is　superior　to　other　methods　in　some　techniques　which　are　flexible　in　dealing　with　convergence.