On the Approximate Solution of the First Boundary Value Problem for $ abla ^4 u = f$
Julius O. Smith · SIAM Journal on Numerical Analysis · 1973
For the equation $ abla ^4 u = f$ in a bounded domain, $\Omega \subset R^n $, with infinitely smooth boundary $\Gamma $, it is shown that the solution u to the boundary value problem which prescribes the function and its normal derivative on $\Gamma $ may be approximated as closely as desired by solving a sequence of Dirichlet problems for Poisson equations in the same domain, provided that the data is sufficiently regular.