In this paper we analyze the three-dimensional Peterlin viscoelastic model. By means of a mixed Galerkin and semigroup approach prove existence weak solutions. Further combining parabolic regularity with relative energy method derive conditional weak-strong uniqueness result.

This paper is an overview of recent developments in the construction of finite element interpolants, which are C-conforming on polygonal domains. In 1975, Wachspress proposed a general method for constructing finite element shape functions on convex polygons. Only recently has renewed interest in such interpolants surfaced in various disciplines including: geometric modeling, computer graphics,...

In this paper, we develop a time and its corresponding spatial discretization scheme, based upon the assumption of a certain weak singularity of IIut(t)llLz(n) = llut112, for the discontinuous Galerkin finite element method for one-dimensional parabolic problems. Optimal convergence rates in both time and spatial variables are obtained. A discussion of automatic time-step control method is also...

In this paper, we are concerned with a viscoelastic wave equation memory term, nonlinear damping and source term. Firstly, using the potential well method combined Galerkin approximation procedure, global weak solutions obtained. Secondly, investigate blow-up of initial positive negative energy, as our result improves earlier ones in [29] [36]. Finally, under some assumptions imposed on coeffic...

In this paper, we considered the improved element-free Galerkin (IEFG) method for solving 2D anisotropic steady-state heat conduction problems. The moving least-squares (IMLS) approximation is used to establish trial function, and penalty applied enforce boundary conditions, thus final discretized equations of IEFG problems can be obtained by combining with corresponding weak form. influences n...

A collocation-Galerkin scheme is proposed for an initial-boundary value problem for a first order hyperbolic equation in one space dimension. The Galerkin equations satisfied by the approximating solution are obtained from a weak-weak formulation of the initial-boundary value problem. The collocation points are taken to be affine images of the roots of the Jacobian polynomials of degree r — \ o...