@article{Lipski_Paszyński_2017, title={One-dimensional fully automatic h-adaptive isogeometric finite element method package}, volume={17}, url={https://journals.agh.edu.pl/csci/article/view/1696}, DOI={10.7494/csci.2016.17.4.439}, abstractNote={<p>This paper deals with an adaptive finite element method originally developed<br />by Prof. Leszek Demkowicz for hierarchical basis functions. In this paper, we<br />investigate the extension of the adaptive algorithm for isogeometric analysis<br />performed with B-spline basis functions. We restrict ourselves to h-adaptivity,<br />since the polynomial order of approximation must be fixed in the isogeometric<br />case. The classical variant of the adaptive FEM algorithm, as delivered by the<br />group of Prof. Demkowicz, is based on a two-grid paradigm, with coarse and<br />fine grids (the latter utilized as a reference solution). The problem is solved independently<br />over a coarse mesh and a fine mesh. The fine-mesh solution is then<br />utilized as a reference to estimate the relative error of the coarse-mesh solution<br />and to decide which elements to refine. Prof. Demkowicz uses hierarchical<br />basis functions, which (though locally providing C p−1 continuity) ensure only<br />C 0 on the interfaces between elements. The CUDA C library described in this<br />paper switches the basis to B-spline functions and proposes a one-dimensional<br />isogeometric version of the h-adaptive FEM algorithm to achieve global C p−1<br />continuity of the solution.</p>}, number={4}, journal={Computer Science}, author={Lipski, Paweł Piotr and Paszyński, Maciej}, year={2017}, month={Jan.}, pages={439} }