A multiscale finite element method for elliptic problems in composite materials and porous media
Journal of Computational Physics
SIAM Journal on Numerical Analysis
Unified Analysis of Discontinuous Galerkin Methods for Elliptic Problems
SIAM Journal on Numerical Analysis
Convergence of the Mimetic Finite Difference Method for Diffusion Problems on Polyhedral Meshes
SIAM Journal on Numerical Analysis
The Fast Solution of Boundary Integral Equations (Mathematical and Analytical Techniques with Applications to Engineering)
Plane Wave Discontinuous Galerkin Methods for the 2D Helmholtz Equation: Analysis of the $p$-Version
SIAM Journal on Numerical Analysis
Residual error estimate for BEM-based FEM on polygonal meshes
Numerische Mathematik
A Simple Algorithm for Maximal Poisson-Disk Sampling in High Dimensions
Computer Graphics Forum
Error estimates for generalized barycentric interpolation
Advances in Computational Mathematics
Arbitrary order Trefftz-like basis functions on polygonal meshes and realization in BEM-based FEM
Computers & Mathematics with Applications
| Hi-index | 7.29 |
The goal of this paper is to generalize a variant of the BEM-based FEM for second order elliptic boundary value problems to three space dimensions. Here, the emphasis lies on polyhedral meshes with polygonal faces, where even non-convex elements are allowed. Due to an implicit definition of the trial functions in the spirit of Trefftz, the strategy yields conforming approximations and is very flexible with respect to the meshes. Thus, it gets into the line of recent developments in several areas. The arising local problems are treated by two dimensional Galerkin schemes coming from finite and boundary element formulations. With the help of a new interpolation operator and its properties, convergence estimates are proven in the H^1- as well as in the L"2-norm. Numerical experiments confirm the theoretical results.