Aguirre, C.G., Madani, A., Mohtar, R. and Haghighi, K. 2007. Deterministic finite element solution of unsteady flow and transport through porous media: Model verification. Canadian Biosystems Engineering/Le génie des biosystèmes au Canada 49: 1.1 1.9. A deterministic finite element solution to predict water flow and nutrient movement through porous media was developed and implemented using Visu...

Interior error estimates are obtained for a low order finite element introduced by Arnold and Falk for the Reissner– Mindlin plates. It is proved that the approximation error of the finite element solution in the interior domain is bounded above by two parts: one measures the local approximability of the exact solution by the finite element space and the other the global approximability of the ...

We present the error analysis of a particular Oldroyd-B type model with the limiting Weissenberg number going to infinity. Assuming a suitable regularity of the exact solution we study the error estimates of a standard finite element method and of a combined finite element/finite volume method. Our theoretical result shows first order convergence of the finite element method and the error of th...

The performance of finite element computation depends strongly on the quality of the geometric mesh and the efficiency of the numerical solution of the linear systems resulting from the discretization of partial differential equation (PDE) models. It is common knowledge that mesh geometry affects not only the approximation error of the finite element solution but also the spectral properties of...

AbstrPct--This paper illustrates some recent advances in finite element procedures that are important for practical engineering analysis. Capabilities to solve large hnite element systems using iterative methods, and some significant advances in finite element procedures for the nonlinear analysis of structures and fluids are demonstrated. The emphasis is on presenting solution results that dem...

in this study, focuses on applying the hp-version for forward modeling. the eit forward solver is normally based on the conventional finite element method (hfem). in h-fem, the polynomial order p of the element shape functions is constant and the element size h, is decreased. to accurately simulate the forward solution with the hfem, a mesh with large number of nodes and elements is usually need...

In this paper, Forchheimer equation is used as the constitutive equation for flow through rockfill, and the non-linear two-dimensional governing equation with free surface is solved by a new finite element method in a fixed grid. The model is verified by applying it to different flow conditions. The first scenario, which is assumed to be one-dimensional with analytical solution available for it...

In this paper, Forchheimer equation is used as the constitutive equation for flow through rockfill, and the non-linear two-dimensional governing equation with free surface is solved by a new finite element method in a fixed grid. The model is verified by applying it to different flow conditions. The first scenario, which is assumed to be one-dimensional with analytical solution available for it...

In this paper we present a finite element discretization of the Joule-heating problem. We prove existence of solution to the discrete formulation and strong convergence of the finite element solution to the weak solution, up to a sub-sequence. We also present numerical examples in three spatial dimensions. The first example demonstrates the convergence of the method in the second example we con...

In the paper, we analyze the L norm error estimate of lower order finite element methods for the fourth order problem. We prove that the best error estimate in the L norm of the finite element solution is of second order, which can not be improved generally. The main ingredients are the saturation condition established for these elements and an identity for the error in the energy norm of the f...