6 research outputs found
A Two-Level Finite Element Discretization of the Streamfunction Formulation of the Stationary Quasi-Geostrophic Equations of the Ocean
In this paper we proposed a two-level finite element discretization of the
nonlinear stationary quasi-geostrophic equations, which model the wind driven
large scale ocean circulation. Optimal error estimates for the two-level finite
element discretization were derived. Numerical experiments for the two-level
algorithm with the Argyris finite element were also carried out. The numerical
results verified the theoretical error estimates and showed that, for the
appropriate scaling between the coarse and fine mesh sizes, the two-level
algorithm significantly decreases the computational time of the standard
one-level algorithm.Comment: Computers and Mathematics with Applications 66 201
Nitsche's method for Kirchhoff plates
We introduce a Nitsche's method for the numerical approximation of the
Kirchhoff-Love plate equation under general Robin-type boundary conditions. We
analyze the method by presenting a priori and a posteriori error estimates in
mesh-dependent norms. Several numerical examples are given to validate the
approach and demonstrate its properties
Code generation for generally mapped finite elements
Many classical finite elements such as the Argyris and Bell elements have long been absent from high-level PDE software. Building on recent theoretical work, we describe how to implement very general finite-element transformations in FInAT and hence into the Firedrake finite-element system. Numerical results evaluate the new elements, comparing them to existing methods for classical problems. For a second-order model problem, we find that new elements give smooth solutions at a mild increase in cost over standard Lagrange elements. For fourth-order problems, however, the newly enabled methods significantly outperform interior penalty formulations. We also give some advanced use cases, solving the nonlinear Cahn-Hilliard equation and some biharmonic eigenvalue problems (including Chladni plates) using C1 discretizations