The standard nonconforming linear Crouzeix-Raviart functions are used on non-interface elements.
end{aligned} (3.21) Noting that (overline{S}_{h}(T subset H^{2}(T)), the above two inequalities both hold on the non-interface element (Tinmathcal {T}_{h}^{n}).
It is also called a non-interface element if Γ intersects with this triangle but does not separate its interior into two nontrivial subsets.
In this paper we propose a new high-order solution framework for interface problems on non-interface-conforming meshes.
The method is then applied to non-interface-conforming meshes using a cut-cell technique, where the interface definition is completely separate from the mesh generation process.
We assume that on non-interface edges, the quantity (sum_{einmathcal{E}^{n}_{h}}int_{e}{betanabla u cdot mathbf {n}_{e}}[v],ds) is not very large which suggests to ignore this term in our scheme.
GFMD uses molecular dynamics to simulate the interaction of the interface's atoms (two layers here), while the non-interface layer, which usually exhibits elastic behaviors, is simulated by the Green's function.
Let (mathcal{T}_{h}={T}) be the usual regular triangulation of the domain Ω. (mathcal{T}_{h}^{i}) and (mathcal{T}_{h}^{n}) denote the collection of interface elements and the collection of the non-interface elements, respectively.
The standard linear Crouzeix-Raviart type finite element space is used on non-interface elements and the piecewise linear Crouzeix-Raviart type immersed finite element (IFE) space is constructed on interface elements.
Many of the magnetostatic/electrostatic field problems encountered in aerospace engineering, such as plasma sheath simulation and ion neutralization process in space, are not confined to finite domain and non-interface problems, but characterized as open boundary and interface problems.
Moreover, the sets of the interface edges and non-interface edges are denoted by (mathcal {E}^{i}_{h}) and (mathcal{E}^{n}_{h}). Obviously, here we have (mathcal {E}_{h}=mathcal{E}^{circ}_{h}cupmathcal{E}^{b}_{h}) and also (mathcal {E}_{h}=mathcal{E}^{i}_{h}cupmathcal{E}^{n}_{h}).
