Beyer, R. P.; LeVeque, R. J. Analysis of a one-dimensional model for the immersed boundary method. (English) Zbl 0762.65052 SIAM J. Numer. Anal. 29, No. 2, 332-364 (1992). 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. Reviewer: S.E.Zhelezovsky (Saratov) Cited in 1 ReviewCited in 93 Documents 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 Keywords:error analysis; discrete delta function; immersed boundary method; Crank- Nicolson method Citations:Zbl 0403.76100 PDFBibTeX XMLCite \textit{R. P. Beyer} and \textit{R. J. LeVeque}, SIAM J. Numer. Anal. 29, No. 2, 332--364 (1992; Zbl 0762.65052) Full Text: DOI Link