Career
He is noted for having designed several remarkable lighthouses in Iceland. These include the lighthouses at Hólmsbergsviti, Gardskagi, Þrídrangaviti and Knarraros. A postage stamp depicting the Vattarnes lighthouse at Reyðarfjörður, which was designed by Axel, was issued in 2013.
Axel was born in Bergsholti in Staðarveit, Snaefellsnessyslu to Sveinn Bjarnason and Sigriður Magnusdóttir.
Axel and Aðalbjorg had one son, Hulda Sveinsson. Axel and Guðrun had one daughter, Solveig Axelsdottir.