This paper is to present a finite volume element(FVE)method based on the bilinear immersed finite element(IFE)for solving the boundary value problems of the diffusion equation with a discontinuous coefficient(interfac...This paper is to present a finite volume element(FVE)method based on the bilinear immersed finite element(IFE)for solving the boundary value problems of the diffusion equation with a discontinuous coefficient(interface problem).This method possesses the usual FVE method’s local conservation property and can use a structured mesh or even the Cartesian mesh to solve a boundary value problem whose coefficient has discontinuity along piecewise smooth nontrivial curves.Numerical examples are provided to demonstrate features of this method.In particular,this method can produce a numerical solution to an interface problem with the usual O(h2)(in L2 norm)and O(h)(in H1 norm)convergence rates.展开更多
基金This work is partially supported by NSF grant DMS-0713763 and NSERC(Canada).
文摘This paper is to present a finite volume element(FVE)method based on the bilinear immersed finite element(IFE)for solving the boundary value problems of the diffusion equation with a discontinuous coefficient(interface problem).This method possesses the usual FVE method’s local conservation property and can use a structured mesh or even the Cartesian mesh to solve a boundary value problem whose coefficient has discontinuity along piecewise smooth nontrivial curves.Numerical examples are provided to demonstrate features of this method.In particular,this method can produce a numerical solution to an interface problem with the usual O(h2)(in L2 norm)and O(h)(in H1 norm)convergence rates.
