[PDF] Top 20 Error Analysis of the Immersed Interface Method for Elliptic Problems with an Interface.

... to problems. Thus, error appears between numerical solutions and exact ...always error analy- sis along with numerical ...smoothing method for discontinuous coefficients does not give very ... See full document

... matched interface and boundary (MIB) based ADI method is proposed for heat equations with a discontinuous coefficient, which is a step forward in this ...the method is only first order accurate in ... See full document

... anisotropic elliptic interface problems, we presented the partially penalty IFE method in [] by adding two penalty terms on the common edges of the adjacent interface elements to ... See full document

... for elliptic interface equations with piecewise constant but discontinuous ...original elliptic equation before using the immersed interface method ... See full document

... order immersed interface method was developed for the elasticity system with an interface based on Cartesian ...the method is still under investi- gation, and the linear solver for the ... See full document

... the interface problem consists of the usual boundary value problem of the diffusion equation, plus jump conditions across the material interface required by pertinent ...the interface is smooth ... See full document

... accurate elliptic solvers using Cartesian grids are presented for three dimen- sional interface problems in which the coefficients, the source term, the solution and its normal flux may be ... See full document

... sharp interface method which can accurately capture dis- continuities in the solution and the ...This method has been used for many problems, such as elliptic interface ... See full document

... mersed interface method ...2D elliptic inter- face problems, Stokes and Navier-Stokes equations with fixed or moving interfaces, and some application problems about two-phase ... See full document

... In this section, several numerical examples are carried out to illustrate our theoretical results. We select the stabilization parameter δ = 1.0 in the first three testing examples, and δ = 0.1 in the last case. The code ... See full document

... control problems (OCPs) governed partial dif- ferential equations are playing an increasingly crucial role in a lot of engineering applications, such as chemical processes, fluid dynamics, medicine, economics, and ... See full document

... Correlation study is conducted for every block of convergence on the correlation of the logarithm of computational error and logarithm of mesh size. More specifically the Pearson Product Moment Correlation ... See full document

... these problems. Using a grid that conforms to the interface is an obvious alternative, for example a structured grid that is deformed in the neighborhood of the interface [7] or an unstructured ... See full document

... the interface at the same time. For general interface problems, a second order accu- rate solution does not necessarily guarantee second order accuracy in its ...the interface even though the ... See full document

... stability analysis has no direct answer for the given ...stability analysis does not work in this situation, because the co- efficients change in a nonsmooth ...energy method or the GKS theory [3, ... See full document

... encounter interface problems when multi-materials with different conductivities, densities, or permeability are ...moving interface problems. Since the interface is moving, a new fitted ... See full document

... The immersed finite element methods incorporate the finite-element discretization into the framework of the immersed-interface method for interface problems; and we therefore ... See full document

... [r] ... See full document

... IB method for elliptic interface problems with general boundary ...IB method for elliptic interface problems with Dirichlet boundary ...IB method is indeed ... See full document

... element method is a very powerful tool in engineering and it has been used widely in solving structural, mechanical, heat transfer, and fluid dynamics problems and many other ...element method ... See full document