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By using a regularization technique, we prove the existence of global in time weak solutions of (1) which is regular and unique for d<\/jats:italic> = 1, 2. Moreover, we propose two fully discrete Finite Element (FE) nonlinear schemes, the first one defined in the variables (u<\/jats:italic>,v<\/jats:italic>) under structured meshes, and the second one by using the auxiliary variable \u03c3<\/jats:italic><\/jats:bold> = \u2207v<\/jats:italic> and defined in general meshes. We prove some unconditional properties for both schemes, such as mass-conservation, solvability, energy-stability and approximated positivity. Finally, we compare the behavior of these schemes with respect to the classical FE backward Euler scheme throughout several numerical simulations and give some conclusions.<\/jats:p>","DOI":"10.1007\/s10444-021-09907-1","type":"journal-article","created":{"date-parts":[[2021,12,10]],"date-time":"2021-12-10T08:05:45Z","timestamp":1639123545000},"update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":7,"title":["A chemorepulsion model with superlinear production: analysis of the continuous problem and two approximately positive and energy-stable schemes"],"prefix":"10.1007","volume":"47","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-5539-5888","authenticated-orcid":false,"given":"F.","family":"Guill\u00e9n-Gonz\u00e1lez","sequence":"first","affiliation":[]},{"given":"M. A.","family":"Rodr\u00edguez-Bellido","sequence":"additional","affiliation":[]},{"given":"D. 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