This　paper　uses　the　simplest　linear　finite　elements　of　the　Galerkin　type　and　gives　a　compact　and　efficient　recurrence　solution　formula　for　equations　of　motion.　Further,　based　on　the　EEP　(Element　Energy　Projection)　super-convergence　technique,　two　critical　techniques,　i.e.　adaptive　time-step　size　and　recovery　of　nodal　displacement　accuracy,　have　been　developed,　enabling　a　linear　finite　element　solution　with　errors　uniformly　distributed　and　satisfying　the　pre-specified　error　tolerance　at　any　moment　in　the　whole　time　domain.　Numerical　examples　of　both　single　and　multiple　degreed　systems　are　given　to　verify　the　validity　of　the　proposed　method.　©　2018,　Engineering　Mechanics　Press.　All　right　reserved.