In this paper we describe and analyze some modified boundary element methods to solve exterior boundary value problems for the Helmholtz equation with either Dirichlet or Neumann boundary conditions. The proposed approach avoids spurious modes even in the case of Lipschitz boundaries. Moreover, the regularisation is done based on boundary integral operators which are already available in standa...

This paper studies mixed finite element approximations to the solution of the viscoelasticity wave equation. Two new transformations are introduced and a corresponding system of first order differential-integral equations is derived. The semi-discrete and full-discrete mixed finite element methods are then proposed for the problem based on the Raviart-Thomas-Nedelec spaces. The optimal error es...

In this paper, the global superconvergence is analysed on two schemes (a mixed finite element scheme and a finite element scheme) for Maxwell’s equations in R3. Such a supercovergence analysis is achieved by means of the technique of integral identity (which has been used in the supercovergence analysis for many other equations and schemes) on a rectangular mesh, and then are generalized into m...

We present a numerical method for the computat ion of discrete solutions of the Plateau Problem. This problem consists of the investigation of minimal surfaces bounded by a prescribed Jordan curve in space. The numerical method allows to compute unstable minimal surfaces with prescribed boundary . It is based on a Boundary Element Method for which asymptotic convergence was proved and which use...

In this paper we prove the L2 convergence rates for a fully discrete finite element procedure for approximating minimal, possibly unstable, surfaces. Originally this problem was studied by G. Dziuk and J. Hutchinson. First they provided convergence rates in the H1 and L2 norms for the boundary integral method. Subsequently they obtained the H1 convergence estimates using a fully discrete finite...

In this paper we present a finite element analysis for a Dirichlet boundary control problem where the Dirichlet control is considered in the energy space H1/2(Γ). As an equivalent norm in H1/2(Γ) we use a norm which is induced by a stabilized hypersingular boundary integral operator. The analysis is based on the mapping properties of the solution operators related to the primal and adjoint boun...

In this paper, we consider the evaluation of flux integral outputs from reduced basis solutions to second-order PDE’s. In order to evaluate such outputs, a lifting function v must be chosen. In the standard finite element context, this choice is not relevant, whereas in the reduced basis context, as we show, it greatly affects the output error. We propose two “good” choices for v, and illustrat...

The damage tolerance behavior of integrally and conventional stiffened panel is investigated based on the fracture mechanics and finite element analysis. The load bearing capability and crack growth characteristic of both types of the stiffened panels having same configuration subjected to distributed tensile load is examined in this paper. A fourteen-stringer stiffened panel is analyzed for a ...

The paper presents a Galerkin approach for the solution of nonlinear beam equations. The approach is energy consistent, i.e., it is shown that the weighted residual integral describes energy flow. The Galerkin approach gives accurate results with less degrees of freedom as compared to low-order finite element formulation. The Galerkin approach also leads to a nonlinear order-reduction technique...

For composite structure, fracture toughness is a dominant parameter when using cohesive laws to predict the nominal strength. In the present study the compact tension test is performed on composites structures and is simulated using FEM. The process of fracture takes places in two sequential stages, crack initiation and crack propagation. The critical energy release rate is determined using the...