[PDF] Top 20 Error estimates of an immersed finite element method for interface problems

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

... In this paper we have proposed a stabilized coupled algorithm for the elliptic interface problem. The main contribution of the present work is the analysis of the optimal error estimates for the ... See full document

... the method for interface problems only with singular sources where the augmented variable is assumed to be ...augmented method and the error estimates are provided in ... See full document

... elliptic interface OCP (1)- (2), which could also be extended to parabolic and hyperbolic ...This method was studied in [5] for solving interface problems and obtained the suboptimal order ... See full document

... The immersed finite element methods incorporate the finite-element discretization into the framework of the immersed-interface method for interface ... See full document

... the problems of the multiple materials or fluids with different densities or conductivities or ...penalty immersed finite element (PIFE) method on triangular grids for anisotropic flow models, in ... See full document

... The rest of this paper is as follows: In Sect. 2, we introduce the optimal control problems and its mixed finite element scheme. Section 2 ends with the definition of the mixed elliptic reconstructions, which ... See full document

... finite element method to deal with fourth order hyperbolic optimal control ...posteriori error estimates and superconvergence of mixed finite element solution for fourth order hyperbolic ... See full document

... control problems, the objective functional contains gradient of the state ...the finite element community, mixed finite element methods should be used for discretization of the state ... See full document

... The paper is organized as follows. In Section , we shall construct the hp finite element approximation for nonlinear parabolic optimal control problems. In Section , we derive hp a posteriori error ... See full document

... elasticity problems that do not involve interfaces. Among them, the finite element method and the boundary integral or boundary element method appear to be very successful, ... See full document

... to problems. Thus, error appears between numerical solutions and exact ...always error analy- sis along with numerical ...the finite difference methods, we have concerned about the accuracy of ... See full document

... in interface conditions, we will use a local coordinates system defined by the normal and tangential directions of the interface at some point on the ...the interface conditions to find the equation ... See full document

... In Chapter 6 , we use the method developed earlier to establish a variational formulation for a class of nonlinear vectorial boundary value problems and to derive error estimates for the[r] ... See full document

... In this section, we shall study the mixed finite element and the backward Euler discretiza- tion approximation of convective diffusion optimal control problems (.)-(.). For the sake of simplicity, we ... See full document

... at finite locations of the computational ...elliptic problems (both linear and nonlinear) and nonmonotone problems and highlighted the various steps needed to derive a priori estimates in the ... See full document

... Abstract. In this paper, a 2D model for the simulation of shallow water flow by convection and diffusion over variable bottom is presented, which is based on a finite volume method over triangular ... See full document

... the problems in engineering applications, an acceptable solution is generally preferred instead of the exact solution of the ...such problems that the complete solution is considered impossible and the ... See full document

... finite element spaces for elliptic equations were analysed in [6] and an adaptive finite element method for stationary surfaces was considered in ...finite element method (SFEM) is to use ... See full document

... nonlinear method in Fig. 2. This study demonstrates that the method with linear crosswind diffusion was outperformed, with respect to the quality of the computed solution, by the nonlinear method ... See full document