1](x, y) is a biharmonic function
that meets equation coinciding with (32) and the function [w.
Biharmonic function w in this case has the sense of Love stress function, through which displacement components [u.
In the problem of the first and second kinds the biharmonic functions should be subordinated to boundary conditions (2) and (3) correspondingly :
h]([GAMMA]) to be the discrete biharmonic function whose dofs on [GAMMA] (cf.
The discrete biharmonic functions enjoy the following minimum energy property.
Let F be either a harmonic function in D or a biharmonic function in D which is not harmonic.
Biharmonic functions arise in a lot of physical situations, particularly in fluid dynamics and elasticity problems, and have many important applications in engineering and biology.
Note that a discrete biharmonic function w = Hw is uniquely defined by the values of all degrees of freedom at nodes in [bar.
h]([OMEGA]) be a discrete biharmonic function, such that [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] on [partial derivative][[OMEGA].
0] be a discrete biharmonic function
such that on any master [[gamma].
j] in the second order case and a discrete biharmonic function
in the fourth order case.
These radial biharmonic functions
suggest the construction of the following thinplate splines.