Abstract
In this paper we present an efficient, accurate and parallelizable direct method for the solution of the (indefinite) linear algebraic systems that arise in the solution of fourth-order partial differential equations (PDEs) using mixed finite element approximations. The method is intended particularly for use when multiple right-hand sides occur, and when high accuracy is required in these solutions. The algorithm is described in some detail and its performance is illustrated through the numerical solution of a biharmonic eigenvalue problem where the smallest eigenpair is approximated using inverse iteration after discretization via the Ciarlet–Raviart mixed finite element method.
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