Equal-order Finite Element Method Research Articles

Mixed Finite Elements for Spatial Regression with PDE Penalization

We study a class of models at the interface between statistics and numerical analysis. Specifically, we consider nonparametric regression models for the estimation of spatial fields from pointwise and noisy observations, which account for problem-specific prior information, described in terms of a partial differential equation governing the phenomenon under study. The prior information is incorporated in the model via a roughness term using a penalized regression framework. We prove the well-posedness of the estimation problem, and we resort to a mixed equal order finite element method for its discretization. Moreover, we prove the well-posedness and the optimal convergence rate of the proposed discretization method. Finally the smoothing technique is extended to the case of areal data, particularly interesting in many applications.

An Efficient Equal-Order Finite-Element Method for Natural Convection in Complex Enclosures

In this article, an efficient and accurate equal-order finite-element method is developed and then incorporated into the finite-element program, ANSYS/FLOTRAN, release 6.0. In this method the systems of linear algebraic equations resulting from the finite-element formulation of the momentum and energy equations are solved implicitly using a fast and robust preconditioned BiCGStab( l ) algorithm. Further, the linkage between the momentum and continuity equations is enhanced through improved pressure-velocity coupling. As a result, no under-relaxation is needed for the pressure equation and large values of under-relaxation are possible for the momentum and energy equations, resulting in a marked improvement in convergence. Both efficiency and accuracy of this method are demonstrated for buoyancy-driven flows in square, semicircular, and triangular cavities at various Rayleigh numbers.

A HYBRID NUMERICAL METHOD FOR NAVIER-STOKES EQUATIONS BASED ON SIMPLE ALGORITHM

Abstract A new numerical approach using both the finite-element method and the control-volume method is proposed for the Navier-Stokes equations. For the momentum equation, the segregated equal-order velocity-pressure formulation has been combined with the streamline upwind Petrov-Galerkin finite-element method using the four-node element. The pressure equation has been obtained by applying the mass conservation principle to an arbitrary-shaped control volume. The present method has been tested for lid-driven cavity flow and natural convection in a square cavity. With comparable computing cost to the finite-volume method, the proposed hybrid numerical method gives accurate results for the Navier-Stokes equations, which are free from the checkerboard-type pressure distribution and retain the merits of equal-order finite-element method.