test the resistance through the element.
The procedure is in the manufacturers service guides, but should be simple for an electrical engineer, electrician, or plumber with a voltohmeter.
Turn off the breaker serving the heater. Use any multi-tester you can - they are cheap. You want to measure ohms or resistence thru the element. Disconnect the wires from the element. Simply put one lead on each wire connection. Not the wire. If you read resistance the element is probably ok. If not it's broken
You should also check the other element and it connection to ground, if one has failed, the other may also need to be replaced. Follow the procedure by KSherlock then check from either wire connection to ground, if there is less than infinite resistance that element should also be replaced.
Hydrae