ASYMPTOTICALLY OPTIMAL INTERFACE SOLVERS FOR THE BIHARMONIC DIRICHLETPROBLEM ON CONVEX POLYGONAL DOMAINS

In this paper we consider an efficient discretization scheme for the b oundary reduction of the biharmonic Dirichlet problem on convex polygo nal domains developed in [6]. We first show that the biharmonic Dirich let problem can be reduced to the solution of a harmonic Dirichlet pro blem and of an equation with the restriction of the Poincare-Steklov o perator. We then propose a mixed FE discretization (by linear elements ) of this equation which admits efficient preconditioning and matrix c ompression resulting in the complexity log epsilon(-1)O(N log(q) N). H ere N is the number of degrees of freedom on the underlying boundary, epsilon > 0 is an error reduction factor, q = 2 or q = 3 for rectangul ar or polygonal boundaries, respectively.