Special finite element methods for a class of second order elliptic problems with rough coefficients
SIAM Journal on Numerical Analysis
A multiscale finite element method for elliptic problems in composite materials and porous media
Journal of Computational Physics
Can a finite element method perform arbitrarily badly?
Mathematics of Computation
Computing
Finite Element Method for Elliptic Problems
Finite Element Method for Elliptic Problems
Highly accurate finite element method for one-dimensional elliptic interface problems
Applied Numerical Mathematics
Immersed finite element methods for 4th order differential equations
Journal of Computational and Applied Mathematics
3D Composite Finite Elements for Elliptic Boundary Value Problems with Discontinuous Coefficients
SIAM Journal on Scientific Computing
Linear and bilinear immersed finite elements for planar elasticity interface problems
Journal of Computational and Applied Mathematics
Efficient collision detection for composite finite element simulation of cuts in deformable bodies
The Visual Computer: International Journal of Computer Graphics
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In this paper, we will introduce composite finite elements for solving elliptic boundary value problems with discontinuous coefficients. The focus is on problems where the geometry of the interfaces between the smooth regions of the coefficients is very complicated.On the other hand, efficient numerical methods such as, e.g., multigrid methods, wavelets, extrapolation, are based on a multi-scale discretization of the problem. In standard finite element methods, the grids have to resolve the structure of the discontinuous coefficients. Thus, straightforward coarse scale discretizations of problems with complicated coefficient jumps are not obvious.In this paper, we define composite finite elements for problems with discontinuous coefficients. These finite elements allow the coarsening of finite element spaces independently of the structure of the discontinuous coefficients. Thus, the multigrid method can be applied to solve the linear system on the fine scale.We focus on the construction of the composite finite elements and the efficient, hierarchical realization of the intergrid transfer operators. Finally, we present some numerical results for the multigrid method based on the composite finite elements (CFE–MG).