The element subroutines in finite element method (FEM) provides enough parallelism to be successfully accelerated by contemporary GPUs. However, their efficient implementation is not straightforward and requires time-consuming exploration of numerous implementation variants. In this paper, we present kernel fusion as an optimization technique and its application for element subroutines. Moreover, we show how the kernel fusion is automated using our source-to-source compiler. We demonstrate the optimization of the element subroutines for FEM model using St.\, Venant-Kirchhoff material. The performance of code generated by our compiler outperforms our previously published hand-tuned implementation by factor of 1.32 -- 1.54 depending on used GPU architecture. Although the optimization techniques are demonstrated on element subroutines for using St.\, Venant-Kirchhoff material, they are generally usable for wider area of computationally-demanding problems.