Abstract In this paper, we propose an efficient approach to solve the fifthorder KdV equations. By using the variational iteration method, the exact solutions of the fifth-order KdV equations are given without the calculation of the complicated Adomian’s polynomials, linearization, discretization, weak nonlinearity assumptions or perturbation theory. Numerical examples are presented that show t...

The evolution of a viscous thin film on a curved geometry is numerically approximated based on the natural time discretization of the underlying gradient flow. This discretization leads to a variational problem to be solved at each time step, which reflects the balance between the decay of the free (gravitational and surface) energy and the viscous dissipation. Both dissipation and energy are d...

Abstract. We present an automated multilevel substructuring (AMLS) method for eigenvalue computations in linear elastodynamics in a variational and algebraic setting. AMLS first recursively partitions the domain of the PDE into a hierarchy of subdomains. Then AMLS recursively generates a subspace for approximating the eigenvectors associated with the smallest eigenvalues by computing partial ei...

We discuss a discretization approach for the p Laplacian equation and a variational inequality associated to fourth order elliptic operators, via a meshless approach based on duality theory. MSC: 35J20, 35J25, 65N99. keywords: nonlinear elliptic equations, Fenchel theorem, approximation, meshless method.

The goal of this paper is the analysis of a non-conforming finite element method for convex variational problems in the presence of the Lavrentiev phenomenon for which conforming finite element methods are known to fail. By contrast, it is shown that the Crouzeix–Raviart finite element discretization always converges to the correct minimizer.

We consider the variational formulation of the electric field integral equation (EFIE) on bounded polyhedral open or closed surfaces. We employ a conforming Galerkin discretization based on divΓ-conforming Raviart-Thomas boundary elements (BEM) of locally variable polynomial degree on shape-regular surface meshes. We establish asymptotic quasi-optimality of Galerkin solutions on sufficiently fi...

We report recent progress in computer simulations of quantum systems described in the path-integral formulation. For the example of the φ quantum chain we show that the accuracy of the simulation may greatly be enhanced by a combination of multigrid update techniques with a refined discretization scheme. This allows us to assess the accuracy of a variational approximation.

This paper presents a mixed variational formulation and its discretization by finite elements of higher-order for the Signorini problem with Tresca friction. To guarantee the unique existence of the solution to the discrete mixed problem, a discrete inf-sup condition is proved. Moreover, a solution scheme based on the dual formulation of the problem is proposed. Numerical results confirm the th...

The paper deals with a topology optimization formulation that uses mixed-finite elements. The discretization scheme adopts not only displacements (as usual) but also stresses as primary variables. Two dual variational formulations based on the HellingerReissner variational principle are presented in continuous and discrete form. The use of this technique and the choice of nodal densities as opt...

We develop a global-in-time variational approach to the time-discretization of rate-independent processes. In particular, we investigate a discrete version of the variational principle based on the weighted energy-dissipation functional introduced in [MO08]. We prove the conditional convergence of time-discrete approximate minimizers to energetic solutions of the time-continuous problem. Moreov...