We deduce discrete compactness of Rellich type for some discontinuous Galerkin finite element methods (DGFEM) including hybrid ones, under fairly general settings on the triangulations and the finite element spaces. We make use of regularity of the solutions to an auxiliary second-order elliptic boundary value problem as well as the error estimates of the associated finite element solutions. Th...

The paper presents a Galerkin approach for the solution of the nonlinear beam equations. Nonlinear beam analysis is required when analyzing helicopter blades or high-aspect-ratio wings. The present analysis improves on earlier solution techniques based on nonlinear finite element approach used in Refs. 1 and 2, and is the ideal choice for beam-like structures undergoing large motion. Furthermor...

Numerical approximations are considered for a mathematical model for miscible displacement influenced by mobile and immobile water. A mixed finite element method is adopted to give a direct approximation of the velocity, the concentration in mobile water is approximated by an alternating direction Galerkin finite element method combined with the method of characteristics and the concentration i...

This paper is concerned with the numerical minimization of energy functionals in BV (Ω) (the space of bounded variation functions) involving total variation for gray-scale 1-dimensional inpainting problem. Applications are shown by finite element method and discontinuous Galerkin method for total variation minimization. We include the numerical examples which show the different recovery image b...

Recently, C. Hofreither, U. Langer and C. Pechstein have analyzed a nonstandard finite element method based on element-local boundary integral operators. The method is able to treat general polyhedral meshes and employs locally PDE-harmonic trial functions. In the previous work, the primal formulation of the method has been analyzed as a perturbed Galerkin scheme, obtaining H error estimates. I...

Abstract. For elliptic interface problems in two and three dimensions, this paper studies a priori and residual-based a posteriori error estimations for the Crouzeix–Raviart nonconforming and the discontinuous Galerkin finite element approximations. It is shown that both the a priori and the a posteriori error estimates are robust with respect to the diffusion coefficient, i.e., constants in th...