Domain decomposition techniques provide a flexible tool for the numerical approximation of partial differential equations. Here, we consider mortar techniques for quadratic finite elements in 3D with different Lagrange multiplier spaces. In particular, we focus on Lagrange multiplier spaces which yield optimal discretization schemes and a locally supported basis for the associated constrained m...

We introduce the Euler-Lagrange cohomology to study the symplectic and multisymplectic structures and their preserving properties in finite and infinite dimensional Lagrangian systems respectively. We also explore their certain difference discrete counterparts in the relevant regularly discretized finite and infinite dimensional Lagrangian systems by means of the difference discrete variasional...

Domain decomposition techniques provide a flexible tool for the numerical approximation of partial differential equations. Here, we consider mortar techniques for quadratic finite elements in 3D with different Lagrange multiplier spaces. In particular, we focus on Lagrange multiplier spaces which yield optimal discretization schemes and a locally supported basis for the associated constrained m...

A new variational principle for an anisotropic elastic formulation in stress space is constructed, the Euler–Lagrange equations of which are the equations of compatibility (in terms of stress), the equilibrium equations and the traction boundary condition. Such a principle can be used to extend recently obtained configurational balance laws in stress space to the case of anisotropy.

The Euler-Lagrange equations of recently introduced chiral action principles are discussed using Lie algebra-valued differential forms. Symmetries of the equations and the chiral description of Einstein’s vacuum equations are presented. A class of Lagrangians, which contains the chiral formulations, is exhibited. † Mathematics Department, King’s College London, Strand, London WC2R 2LS, UK 1

This paper gives an efficient numerical method for solving the nonlinear system of Volterra-Fredholm integral equations. A Legendre-spectral method based on the Legendre integration Gauss points and Lagrange interpolation is proposed to convert the nonlinear integral equations to a nonlinear system of equations where the solution leads to the values of unknown functions at collocation points.

An error analysis is presented for the approximation of the statiornary Stokes equations by a finite element method using Lagrange multipliers.

These equations are called Lagrange–Charpit equations. In interpreting these equations, it is convenient to allow zero denominators. For example, if Fp = 0, these equations require that dx = 0; that is, the denominator being zero just means that the numerator is also zero. Assume that from equations (1) and (2) one can derive a new equation (3) φ(x, y, u, p, q) = a, ∗Written for the course Math...

In this paper, an analysis of 3-dimensional problem using a fictitious domain method based on distributed Lagrange multiplier is discussed. Using this approach allows us to compute moving boundary problems successfully. First of all, how to use a fictitious domain method using navier stokes equations is explained. Next, incompressible viscous fluid around circular cylinder and ball are restrict...