Abstract
•PetIGA-MF is a framework that uses discrete differential forms based on B-splines.•We solve viscous flows such as Darcy, Stokes, Brinkman, and Navier–Stokes equations.•Several convergence benchmarks show an exact agreement with a priori error estimates.•Benchmark tests show no superconvergence for pressure when using distorted meshes.•Promising results for reduced quadrature schemes on divergence conforming spaces.
We describe a high-performance solution framework for isogeometric discrete differential forms based on B-splines: PetIGA-MF. Built on top of PetIGA, an open-source library we have built and developed over the last decade, PetIGA-MF is a general multi-field discretization tool. To test the capabilities of our implementation, we solve different viscous flow problems such as Darcy, Stokes, Brinkman, and Navier–Stokes equations. Several convergence benchmarks based on manufactured solutions are presented assuring optimal convergence rates of the approximations, showing the accuracy and robustness of our solver.