# biharmonic function

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## biharmonic function

[¦bī·här′män·ik ′fəŋk·shən]
(mathematics)
A solution to the partial differential equation Δ2 u (x,y,z) = 0, where Δ is the Laplacian operator; occurs frequently in problems in electrostatics.
References in periodicals archive ?
27] --, Two-level non-overlapping Schwarz preconditioners for a discontinuous Galerkin approximation of the biharmonic equation, J.
SULI, A priori error analysis for the hp-version of the discontinuous Galerkin finite element method for the biharmonic equation, Comput.
Particularly, for the inhomogeneous biharmonic equation, analogous results are presented in [16,18].
Begehr, Dirichlet problems for the biharmonic equation, Gen.
Thus, we have to solve the biharmonic equation [[DELTA].
The solutions of the above biharmonic equation which do not depends on [theta] (also called radial) satisfy the equation [([[partial derivative].
the controlled heat equation which represents a boundary reaction in diffusion of chemicals [12], the two dimensional biharmonic equation in a semi-infinite strip [5, 11], dynamic processes in chemical reactors [15] and deformed Pohlmeyer equation [21].
GOMILKO, A Dirichlet problem for the biharmonic equation in a semi-infinite strip, J.
PIRONNEAU, Numerical methods for the first biharmonic equation and for the two-dimensional Stokes problem, SIAM Rev.
additive Schwarz preconditioner, mixed finite elements, biharmonic equation, domain decomposition, mesh dependent norms
Consider the following variational problem for the biharmonic equation with homogeneous Dirichlet boundary conditions: Find u [member of] [H.
of Mississippi) discuss the Trefftz method for collocation by describing coupling techniques, biharmonic equations and combinations of collocation and finite element methods for advanced students in mathematics.

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