We study spatially semidiscrete and fully discrete finite volume element methods for the homogeneous heat equation with homogeneous Dirichlet boundary conditions and derive error estimates for smooth and nonsmooth initial data. We show that the results of our earlier work [Math. Comp. 81 (2012), 1–20] for the lumped mass method carry over to the present situation. In particular, in order for er...

Practical engineering problems in heat transfer and fluid flow involve one or more governing equations, together with some boundary conditions over a domain. The domain is often complex and non-uniform. The ability to use a mesh of finite elements to accurately discretise domain of any size and shape makes the finite element method a powerful tool to numerically analyse problems in these areas....

We analyze the flux conservation property of the finite element method. It is shown that the finite element solution does approximate the flux locally in the optimal order, i.e., the same order as that of the nodal interpolation operator. We propose two methods, post-processing the finite element solutions locally. The new solutions, remaining as optimal-order solutions, are flux-conserving ele...

The present work is a detailed study of the connections between microstructural instabilities and their macroscopic manifestations — as captured through the effective properties — in finitely strained fiber-reinforced elastomers, subjected to finite, planestrain deformations normal to the fiber direction. The work, which is a complement to a previous and analogous investigation by the same auth...

Finite element formulations based generally on classical beam theories such as Euler-Bernoulli or Timoshenko. Sometimes, these two formulations could be problematic expressed in terms of restrictions of Euler-Bernoulli beam theory, in case of thicker beams due to non-consideration of transverse shear; phenomenon that is known as shear locking characterized the Timoshenko beam theory, in case of...

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...

Numerical modeling of machining processes is of significance in the parametric analysis and optimization of their performance. In this paper, a finite element-based model of abrasive waterjet (AWJ) cutting of a ductile material is presented with the help of an explicit, nonlinear finite element method. In this model, both solid-solid interaction and fluid-structure interaction are considered. T...

Computational modelling has received significant attention in the research community over the past few decades due to its pronounced contribution in better understanding of the nature, as well as in the development of advanced technologies. The modelling of more and more complex transport physical systems helps the community to address important issues, like identification of environmental prob...

Currently used finite volume methods are essentially low order methods. In this paper, we present a systematic way to derive higher order finite volume schemes from higher order mixed finite element methods. Mostly for convenience but sometimes from necessity, our procedure starts from the hybridization of the mixed method. It then approximates the inner product of vector functions by an approp...

the transport of dissolved contaminants in groundwater is usually described by the advectiondispersion equation with reaction. several numerical methods for solving the one-dimensional are availableincluding finite difference methods, finite volume methods, and finite element methods. stringent conditions,such as small peclet (pe) and courant (cr) numbers, must be satisfied to ensure the accura...