Assume that has a closed convex cone and that has interior points in, that is, with the interior and the boundary of in.
Let Ω ¯, intΩ, and ∂ Ω denote the closure, the interior, and the boundary of Ω in X, respectively.
As usual, if a set, then intω and ∂ω denote the interior and the boundary of ω, respectively.
For each and each we set, and we let, and denote, respectively, the closure, the interior, and the boundary of with respect to in.
Finally, we end this section with presenting a necessary auxiliary result concerning a higher integrability result for (1.1) in the interior and the boundary version, see [35].
A modified, Laplacian-based interpolation scheme is developed that conserves mass while interpolating values onto nodes that join the cell interior as the boundary moves.
Laminates with finite dimensions are considered and full three-dimensional stresses in the interior and the boundary-layer regions are calculated.
In the ABdC-N scheme (4) for solving the quanto option pricing model is alternatively applied the classical explicit and the implicit scheme at the interior boundary point; then the truncation error of interior boundary point also can achieve a second order.
The interior temperature T i is found by averaging the temperature in the middle part of the interior to exclude the boundary effects.
The resulting solutions are verified with the continuity conditions for the normal and shear stresses along the interior boundary of the matrix.
