Here the outward normal derivative
is [mathematical expression not reproducible]; then
To translate the condition to reference coordinates, we again use the chain rule to write the normal derivative
as a combination of change of variables terms and derivatives in parameter space (by inverting the Jacobian of the mapping [f.
8) is a integral for determining the potential [PHI] on the flapping hydrofoil surface SB and the normal derivative
[partial derivative]/[partial derivative][n.
Note that [partial derivative][OMEGA] is part of the interface because the boundary condition for the normal derivative
is only enforced weakly through the penalty term in (1.
x] is the normal derivative
of u at x, f : [OMEGA] [right arrow] R, and g, [g.
At the outlet, the uniform axial velocity was used to ensure continuity, and tangential velocities were computed from a zero normal derivative
Then the Dirichlet-Neumann operator R([Lambda]) maps a function [Phi](x) defined on [Gamma] to the outward normal derivative
of the solution u(x) of the problem
Here [partial derivative]/[partial derivative]v = v x [nabla] is the operator of normal derivative
on [partial derivative]S, v is the outward unit normal vector to [partial derivative]S, and [f.
m, i] and can have nonzero trace of the normal derivative
The function value and its normal derivative
on the boundary, [PHI](Q) and ([partial derivative]/[partial derivative]n)[PHI](Q), are already known after the evaluation of (4).
where [DELTA] denotes the Laplacian operator and [partial derivative]/[partial derivative]v is the normal derivative
at the boundary of [OMEGA].
j] to be the function whose normal derivative
at p is 1 and takes the value zero for all other nodal variables, and (iii) [[delta].