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In this work we present a new WENO b-spline based quasi-interpolationalgorithm. The novelty of this construction resides in the application of theWENO weights to the b-spline functions, that are a partition of unity, insteadto the coefficients that multiply the b-spline functions of the spline. Theresult obtained conserves the smoothness of the original spline and presentsadaption to discontinuities in the function. Another new idea that we introducein this work is the use of different base weight functions from those proposedin classical WENO algorithms. Apart from introducing the construction of thenew algorithms, we present theoretical results regarding the order of accuracyobtained at smooth zones and close to the discontinuity, as well as theoreticalconsiderations about how to design the new weight functions. Through a tensorproduct strategy, we extend our results to several dimensions. In order tocheck the theoretical results obtained, we present an extended battery ofnumerical experiments in one, two and tree dimensions that support ourconclussions.

Non-linear WENO B-spline based approximation method