In no particular order, I'll add more as I think of them.
- SIAM Journal on Scientific Computing
- Journal of Scientific Computing
- Journal of Computational Physics
- Computer Methods in Applied Mechanics and Engineering
- International Journal of Numerical Methods in Engineering
- AIAA conference proceedings
- Transactions on Mathematical Software
- Computers and Structures
- Acta Numerica
- Numerische Mathematik
- SIAM Journal on Numerical Analysis
- Mathematics of Computation
Also, many application-specific journals have papers on computational methods. It is definitely worth watching appropriate sections of the arXiv.
Before Google Reader killed sharing, we had a group of about 30 people that would monitor different journals and share relevant papers to discuss. We are now, begrudgingly, using Google+ and Reddit for that purpose.