In 2005 Bartel finished equal first with Zoltan Gyimesi in the inaugural EU Individual Open Chess Championship in Cork.

In 2007, he tied for 1st–6th with Vitali Golod, Zahar Efimenko, Yuri Yakovich, Michael Roiz and Mikhail Kobalia in the 16th Monarch Assurance Isle of Man International tournament, as first on tie-break.

[3] In February 2012, Bartel tied for 1st–3rd with Anton Korobov and Pavel Eljanov in the 11th Aeroflot Open, winning the prestigious event on tie-break.

[4] In August 2017, Bartel won the traditional Open (Master Tournament) at the Biel Chess Festival (50th and jubilee edition), on tie-break above Vladimir Baklan.

He played for Czech team "G-Team Nový Bor" that won the 2013 European Chess Club Cup in Rhodes.