A finite element method is developed for approximating the solution of the Dirichlet problem for the biharmonic operator, as a canonical example of a higher order elliptic boundary value problem. The solution is approximated by special choices of classes of discontinuous functions, piecewise polynomial functions, by virtue of a special variational formulation of the boundary value problem. The ...

Inverse boundary data transmission Cauchy type problems for two dimensional elliptic PDE can be efficiently approached using best constrained approximation schemes in Hardy (Hilbert) classes of analytic functions bounded on the domain’s boundary. Such recovery results and algorithms generalize the classical planar links between harmonic and analytic functions (of the complex variable). Specific...