This paper presents the results of nonlinear numerical simulations carried out to analyze rainwater infiltration through a road embankment structure using the finite element method (FEM) technique. The analysis of this paper includes a simplification of a crosssectional road embankment located in Santander (Northern Spain) and considers different realistic hydraulic material parameters, accordi...

Based on homotopy, which is a basic concept in topology, a general analytic method (namely the homotopy analysis method) is proposed to obtain series solutions of nonlinear differential equations. Different from perturbation techniques, this approach is independent of small/large physical parameters. Besides, different from all previous analytic methods, it provides us with a simple way to adju...

We prove the convergence of an adaptive linear finite element method for computing eigenvalues and eigenfunctions of second order symmetric elliptic partial differential operators. The weak form is assumed to yield a bilinear form which is bounded and coercive in H1. Each step of the adaptive procedure refines elements in which a standard a posteriori error estimator is large and also refines e...

This paper presents a 3-dimensional finite element formulation for predicting the behaviour of complex umbilical cross-sections exposed to loading from tension, torque, internal and external pressure including bending. Helically wound armours and tubes are treated as thin and slender beams formulated within the framework of small strains but large displacements, applying the principle of virtua...

In classical tsunami-generation techniques, one neglects the dynamic sea bed displacement resulting from fracturing of a seismic fault. The present study takes into account these dynamic effects. Earth’s crust is assumed to be a Kelvin-Voigt material. The seismic source is assumed to be a dislocation in a viscoelastic medium. The fluid motion is described by the classical nonlinear shallow wate...

A 3-dimensional finite element algorithm for modeling nonlinear frictional contact behaviours between deformable bodies with the node-to-point contact element strategy has been proposed and applied here to investigate stress evolution processes of a nonlinear frictional contact system. The numerical results of a typical intra-plate fault bend model demonstrate the efficiency and usefulness of t...

In this work, we present a numerical framework to simulate high temperature superconductor devices. We select the so-called H-formulation, which uses the magnetic field as a state variable, in order to develop an augmented formulation that guarantees the divergence-free condition. However, nodal elements fail in the H−formulation modelling of electromagnetic fields along interfaces between regi...

We present an implementation of Böhmer’s finite element method for fully nonlinear elliptic partial differential equations on convex polygonal domains, based on a modified Argyris element and BernsteinBézier techniques. Our numerical experiments for several test problems, involving the classical Monge-Ampère equation and an unconditionally elliptic equation, confirm the convergence and error bo...

In the course of this paper, the Optimal Homotopy Asymptotic Method (OHAM) introduced by Marica is applied to solve linear and nonlinear boundary value problems both for fourth-order integro-differential equations. The following analysis is accompanied by numerical examples whose results show that the Optimal Homotopy Asymptotic Method is highly accurate, convenient and relatively efficient for...

where Ω is a bounded domain in Rn (1 ≤ n ≤ 3), f is a nonlinear map.We use the homogeneous Sobolev space H1 0 (Ω)(≡ H1 0 ) for the solution of (1). Also some appropriate assumptions are imposed on the map f . In order to treat the problem as the finite procedure, we use a finite element subspace Sh of H1 0 with mesh size h. Denoting the inner product on L2(Ω) by (·, ·), we define the H1 0 -proj...