We develop a stability and convergence theory for the Ultra Weak Variational Formulation (UWVF) of a highly indefinite Helmholtz problem in Rd, d ∈ {1, 2, 3}. The theory covers conforming as well as nonconforming generalized finite element methods. In contrast to conventional Galerkin methods where a minimal resolution condition is necessary to guarantee the unique solvability, it is proved tha...

In the present study, the three-dimensional elastic discrete element method (DEM) and the elastic finite element method (FEM) analysis were, respectively, applied to the randomly distributed identical spheres as a granular target and to the cylindrical projectiles in order to clarify dynamic response during penetration. In the target, it was found that highly densified region was formed just ah...

In the automotive industry, predicting noise during design cycle is a necessary step. Well-known methods exist to answer this issue in low frequency domain. Among these, Finite Element Methods, adapted to closed domains, are quite easy to implement whereas Boundary Element Methods are more adapted to infinite domains, but may induce singularity problems. In this article, the described method, t...

In this paper, we study the semi-discrete Galerkin finite element method for parabolic equations with Lipschitz continuous coefficients. We prove the maximumnorm stability of the semigroup generated by the corresponding elliptic finite element operator, and prove the space-time stability of the parabolic projection onto the finite element space in L∞(QT ) and L p((0, T ); Lq ( )), 1 < p, q < ∞....

The stability and convergence of nonconforming hp finite-element methods, in particular, the mortar finite-element method and its variants, are established based on a new stability measure for these methods. Using a generalized eigenvalue analysis, estimates for this measure are computed numerically. Our numerical results demonstrate that these nonconforming methods prove to be good candidates ...

This paper presents a simple method based on strain energy density criterion to study the crack initiation angle by finite element method under biaxial loading condition. The crack surface relative displacement method is used to eliminate the calculation of the stress intensity factors which are normally required. The analysis is performed using higher order four node quadrilateral element. The...