[PDF] Top 20 Immersed-Interface Finite-Element Methods for Elliptic and Elasticity Interface Problems

... Elasticity interface problems (1.7)– (1.10) with such jump conditions often occur in material science. For example, in [22], they simulate the diffusional evolution of microstructure in stressed ... See full document

... and elasticity problem with interfaces using the Galerkin finite element method [4, ...the finite element method using body-fitted ...several finite element methods ... See full document

... For elliptic interface problems, the resulting finite difference scheme is the standard five-point central scheme at regular grid points, while it is a compact nine-point scheme at irregular ... See full document

... numerical methods for solving general elasticity problems that do not involve ...the finite element method and the boundary integral or boundary element method appear to be very ... See full document

... In recent years, the immersed finite element (IFE) methods have been studied and found to be very effective for solving elliptic interface problems. The method was proposed on 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

... mesh methods in the literature, for instance, the extended fi- nite element method [5], the unfitted Nitsche’s finite element method [6], the immersed interface method [9, 13], the ... See full document

... linear elasticity—so that geometric nonlinearities become ...the elliptic integrals, but the main achievement concerns the Lauricella F D 3 hypergeometric functions use for solving elasticity ... See full document

... numerical methods are approximating solutions to ...numerical methods. In Section 1.4, when we discuss the finite difference methods, we have concerned about the accuracy of ...specific ... See full document

... linear element has been applied to many ...For interface problems, traditional finite element methods use body-fitted meshes or partition along the boundary or ...finite element ... See full document

... fitted finite element methods, see [2], for one example; the ghost fluid method (GFM) [12] (which is first order accurate in the infinity norm but has a sym- metric linear system); fast solvers based ... See full document

... The results obtained for the two mesh cases (regular and distorted) are listed in Table 2. The results in the case of the distorted mesh (Fig.6c) confirm the excellent performance of element Q4SBE5. In this case, ... See full document

... control problems with objective functionals that contain point evaluations of the ...numerical methods for solving ...of elliptic variational ... See full document

... In Chapter 5, which is based on work we have done in Dedner and Madhavan [2014a], we derive a dual weighted residual-based a posteriori error estimate for the surface IP method considered in Chapter 4, restricting ... See full document

... of immersed finite element methods is the loss of numerical stability in cases where the intersection of a shape function support with the physical domain becomes very ... See full document

... The finite element analyses presented here were based on a perfect fit between the implant and the distal femur because Boolean operations were used to simulate the ...bone interface would provide a ... See full document

... by interface wave which propagate along the shrink fit boundary of reactor head is proposed in this ...proposed interface wave can propagate a long distance from the fixed transducer ...and interface ... See full document

... related problems. For example, the boundary value problems on an irregular ...value problems on irregular domains, many challenges exist in direct discretization at the intersections between the ... See full document

... Although the type and number of TV services have changed significantly, few studies have addressed the TV user interface even though there are clear challenges in the use of TV by consumers. It seems that TV ... See full document

... computational methods have become essential tools for biomedical ...computational methods to several biomedical ...biomedical problems that can be addressed through computation, we describe several ... See full document