We propose and analyze volume-preserving parametric finite element methods for surface diffusion, conserved mean curvature flow an intermediate evolution law in axisymmetric setting. The weak formulations are presented terms of the generating curves surfaces. proposed numerical based on piecewise linear elements. constructed fully practical schemes satisfy conservation enclosed volume. In addit...

In this paper, we analyze a scheme for the time-dependent variable density Navier-Stokes equations. The algorithm is implicit in time, and the space approximation is based on a low-order staggered non-conforming finite element, the so-called Rannacher-Turek element. The convection term in the momentum balance equation is discretized by a finite volume technique, in such a way that a solution ob...

B. Wang, Z. G. Yang, X. F. Zhang, Y. T. Wang, C. P. Nie, Q. Liu, State Key Laboratory of Advanced Metallurgy, University of Science and Technology Beijing, Beijing, China Z. G. Yang, Special Steel Plant, Laiwu Iron & Steel Co. Ltd., Laiwu, China B. Wang, H. B. Dong, Department of Engineering, University of Leicester, Leicester, UK In the current study, a 260 mm × 300 mm bloom mould was investig...

This paper describes a numerical solution for two dimensional partial differential equations modeling (or arising from) a fluid flow and transport phenomena. The diffusion equation is discretized by the mixed hybrid finite element method. The saturation equation is solved by a finite volume method. We start with incompressible single-phase flow and move step-bystep to the black-oil model and co...

We develop a finite element discretization for the weakly symmetric equations of linear elasticity on tetrahedral meshes. The finite element combines, for r ≥ 0, discontinuous polynomials of r for the displacement, H(div)-conforming polynomials of order r+1 for the stress, and H(curl)-conforming polynomials of order r + 1 for the vector representation of the multiplier. We prove that this tripl...

Abstract. We show stability and consistency of the linear semi-implicit complementary volume numerical scheme for solving the regularized, in the sense of Evans and Spruck, mean curvature flow equation in the level set formulation. The numerical method is based on the finite volume methodology using so-called complementary volumes to a finite element triangulation. The scheme gives solution in ...

In this paper we utilize affine biquadratic elements and a two-step temporal discretization to develop a finite volume element method for parabolic problems on quadrilateral meshes. The method is proved to have an optimal order convergence rate in L2(0, T ; H1(Ω)) under the ‘asymptotically parallelogram’ mesh assumption. Numerical experiments that corroborate the theoretical analysis are also p...

We propose and analyze a combined finite volume–nonconforming finite element scheme on general meshes to simulate the two compressible phase flow in porous media. The diffusion term, which can be anisotropic and heterogeneous, is discretized by piecewise linear nonconforming triangular finite elements. The other terms are discretized by means of a cell-centered finite volume scheme on a dual me...

In this paper numerical technique has been used to solve multidimensional unsteady state heat conduction equation with Dirichlet boundary conditions. We focus on finite volume numerical technique for solution of multidimensional time dependent heat conduction problems. Finally, the efficiency of this technique is tested for some heat conduction problems with known analytical solutions and the n...