The present invention relates to composite elements comprising a profile and an insulating core enclosed at least to some extent by the profile, where the insulating core is composed of an organic porous material which has a thermal conductivity in the range from 13 to 30 mW/m*K, determined in accordance with DIN 12667, and a compressive strength of more than 0.20 N/mm2, determined in accordance with DIN 53421, processes for producing composite elements of this type, and the use of a composite element of this type for producing windows, doors, refrigerators, and chest freezers, or elements for facade construction.