This paper presents an isogeometric local h-refinement algorithm based on localized multigrid resolution dedicated to computational mechanics. This algorithm leads to a solution on a quasi optimal refined mesh initially unknown for a given precision criterion. Moreover, it allows us to circumvent the obstacle of refinement of non-straight geometric boundaries existing in full multigrid algorithms with isoparametric finite element analysis. (C) 2015 Elsevier B.V. All rights reserved.