Super-convergence and post-processing for mixed finite element approximations of the wave equation

A Priori Error Estimates for Mixed Finite Element Approximations of the Acoustic Wave Equation

In this paper we derive optimal a priori L∞(L2) error estimates for mixed finite element displacement formulations of the acoustic wave equation. The computational complexity of this approach is equivalent to the traditional mixed finite element formulations of the second order hyperbolic equations in which the primary unknowns are pressure and the gradient of pressure. However, the displacemen...

Error Estimates for Mixed Finite Element Approximations of the Viscoelasticity Wave Equation

This paper studies mixed finite element approximations to the solution of the viscoelasticity wave equation. Two new transformations are introduced and a corresponding system of first order differential-integral equations is derived. The semi-discrete and full-discrete mixed finite element methods are then proposed for the problem based on the Raviart-Thomas-Nedelec spaces. The optimal error es...

Convergence of the discrete free boundaries for finite element approximations

Stability and Convergence of a Second Order Mixed Finite Element Method for the Cahn-Hilliard Equation

In this paper we devise and analyze an unconditionally stable, second-order-in-time numerical scheme for the Cahn-Hilliard equation in two and three space dimensions. We prove that our two-step scheme is unconditionally energy stable and unconditionally uniquely solvable. Furthermore, we show that the discrete phase variable is bounded in L∞ (0, T ;L∞) and the discrete chemical potential is bou...

Posteriorierror Estimator for the Finite Element Methodwith Super Convergence

When the nite element solution of a variational problem possesses certain super convergence properties, it is possible very inexpensively to obtain a correction term providing an additional order of approximation of the solution. The correction can be used for error estimation locally or globally in whatever norm is preferred, or if no error estimation is wanted it can be used for postprocessin...