SIAM Journal on Numerical Analysis
On a FEM--BEM Formulation for an Exterior Quasilinear Problem in the Plane
SIAM Journal on Numerical Analysis
A Fully Discrete BEM-FEM for the Exterior Stokes Problem in the Plane
SIAM Journal on Numerical Analysis
A combination of spectral and finite elements for an exterior problem in the plane
Applied Numerical Mathematics
SIAM Journal on Numerical Analysis
Boundary-Conforming Discontinuous Galerkin Methods via Extensions from Subdomains
Journal of Scientific Computing
The Validity of Johnson-Nédélec's BEM-FEM Coupling on Polygonal Interfaces
SIAM Journal on Numerical Analysis
Relaxing the hypotheses of Bielak–MacCamy’s BEM–FEM coupling
Numerische Mathematik
Solving Dirichlet Boundary-value Problems on Curved Domains by Extensions from Subdomains
SIAM Journal on Scientific Computing
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We introduce a new technique for numerically solving exterior Dirichlet boundary-value problems for second-order elliptic equations. It consists of coupling a hybridizable discontinuous Galerkin (HDG) method used for solving the so-called interior problem on a bounded region containing the support of the source term, with a boundary element method (BEM) for solving the problem exterior to that region. The novelty is that the BEM is defined on a suitably chosen, smooth artificial boundary whereas the HDG method is defined on a polyhedral subdomain. Because of the choice of the artificial boundary, we can take advantage of the spectral convergence of the BEM solution and of the simplicity of the corresponding equations. Because the HDG method is defined on a polyhedral subdomain, there is no need to try to fit the mesh to the artificial boundary. Instead, the HDG is coupled at a distance with the BEM by using simple Dirichlet-to-Neumann operators defined in the region between the artificial boundary and the polyhedral subdomain. Numerical experiments displaying the performance of the new technique are presented. Optimal orders of convergence are obtained even though the distance between the artificial boundary and the polyhedral domain is of order $h$.