## Analysis of a one-dimensional model for the immersed boundary method.(English)Zbl 0762.65052

The accuracy of C. S. Peskin’s immersed boundary method [J. Comput. Phys. 25, 220-252 (1977; Zbl 0403.76100)] is analyzed for one-dimensional model problems. Differential equations of the form $$u_ t=u_{xx}+c(t)\delta(x-\alpha(t))$$ are considered. The delta function $$\delta(x)$$ is replaced by its discrete approximation and the obtained equation is solved by a Crank-Nicolson method on a uniform grid.

### MSC:

 65M06 Finite difference methods for initial value and initial-boundary value problems involving PDEs 65M12 Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs 35K15 Initial value problems for second-order parabolic equations 76D05 Navier-Stokes equations for incompressible viscous fluids 76Z05 Physiological flows

Zbl 0403.76100
Full Text: