Isogeometric Residual Minimization Method (iGRM) for Stokes and Time-Dependent Stokes Problems
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We investigate the application of the residual minimization method (RM) to stabilize the non-stationary Stokes problem. We discretize the trial and test spaces with higher continuity B-spline basis functions from isogeometric analysis (IGA) on a regular patch of elements. We first consider the RM with IGA to stabilize H^1_0, L^2_0 formulation of the stationary Stokes problem. We call our method the isoGeometric Residual Minimization (iGRM). Then, we focus on the non-stationary Stokes problem discretized with IGA in space. We employ a time integration scheme that preserves the Kronecker product structure of the matrix and we use RM to stabilize the problem in every time step. We propose a linear computational cost solver utilizing the Kronecker product structure of the iGRM system. We test our method on a manufactured solution problem and the cavity flow problem.
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