Stability and Convergence of a Regularized Immersed Boundary Method under Dynamic Cartesian Refinement. Part I: Fixed Geometry
We analyze a conforming variational immersed boundary discretization of the two-dimensional unsteady Stokes equations with a fixed interface. Exactly divergence-free velocities are obtained from Cartesian bicubic Hermite streamfunctions; regularized surface moments impose the boundary condition, and backward Euler time stepping uses constrained orthogonal transfer. Arbitrary local fine-scale enrichments may be added or removed at every step while the complete coarse space is retained. For homogeneous interface data, a common coarse comparison family yields an exact energy identity, a…
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