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Most variational forms of isogeometric analysis use highly-continuous basisfunctions for both trial and test spaces. For a partial differential equationwith a smooth solution, isogeometric analysis with highly-continuous basisfunctions for trial space results in excellent discrete approximations of thesolution. However, we observe that high continuity for test spaces is notnecessary. In this work, we present a framework which uses highly-continuousB-splines for the trial spaces and basis functions with minimal regularity andpossibly lower order polynomials for the test spaces. To realize this goal, weadopt the residual minimization methodology. We pose the problem in a mixedformulation, which results in a system governing both the solution and a Rieszrepresentation of the residual. We present various variational formulationswhich are variationally-stable and verify their equivalence numerically vianumerical tests.

Residual minimization for isogeometric analysis in reduced and mixed forms