We propose an efficient computational method to simulate two-phase flow in fractured porous media. Instead of refining the grid to capture the flow along the faults or fractures, we represent them as immersed interfaces with reduced model for the flow and suitable coupling conditions. We allow for non matching grids between the porous matrix and the fracture to increase the flexibility of the m...

1. Lax Equivalence Theorem 1 2. Abstract error analysis 2 3. Application: Finite Difference Method 3 4. Application: Finite Element Method 4 5. Application: Conforming Discretization of Variational Problems 5 6. Application: Perturbed Discretization 6 7. Application: Nonconforming Finite Element Methods 8 8. Application: Finite Volume Method 8 9. Application: Superconvergence of linear finite e...

1. Lax equivalence theorem 1 2. Abstract error analysis 2 3. Application: Finite difference method 3 4. Application: Finite element method 4 5. Application: Conforming Discretization of Variational Problems 5 6. Application: Perturbed Discretization 6 7. Application: Nonconforming finite element methods 7 8. Application: Finite volume method 7 9. Application: Superconvergence of linear finite e...

In this paper a systematic approach of repairing polygonal meshes is developed for volume meshing, which can then be used in finite element analyses. All poor-quality elements are classified into three general categories: point element, line element, and overlapped element. A robust iterative scheme is proposed to remove all poor-quality elements progressively, leading to a successful volume me...

We introduce a new class of higher order mixed finite volume methods for elliptic problems. We start from the usual way of changing the given equation into a mixed system using the Darcy’s law, u = −K∇p. By integrating the system of equations with some judiciously chosen test spaces on each element, we define new mixed finite volume methods of higher order. We show that these new schemes are eq...

In this research, an efficient Galerkin Finite Volume Method (GFVM) along with the h–refinement adaptive process and post–processing error estimation analysis is presented for fracture analysis. The adaptive strategy is used to produce more accurate solution with the least computational cost. To investigate the accuracy and efficiency of the developed model, the GFVM is compared with two versio...

In this work, a stabilized characteristic finite volume method for the time-dependent Navier-Stokes equations is investigated based on the lowest equal-order finite element pair. The temporal differentiation and advection term are dealt with by characteristic scheme. Stability of the numerical solution is derived under some regularity assumptions. Optimal error estimates of the velocity and pre...

nanocomposite materials have recently attracted increasing interests in the field of modelling. finite element modelling can be used for computation of bulk properties of polymer/clay nanocomposites. in this study, by   considering the structure of a nano-composite material, a quasi real model is proposed. the model has been used to predict the elastic constants by selection of suitable element...

Pulmonary contusion is the most commonly identified thoracic soft tissue injury in an automobile crash and after blunt chest trauma and affects 10-17% of all trauma admissions. The mortality associated with pulmonary contusions is significant and is estimated to be 10-25%. Thus, there is a need to develop a finite element model based injury metric for pulmonary contusion for the purpose of pred...