We propose and analyze a symmetric weighted interior penalty (SWIP) method to approximate in a Discontinuous Galerkin framework advection-diffusion equations with anisotropic and discontinuous diffusivity. The originality of the method consists in the use of diffusivity-dependent weighted averages to better cope with locally small diffusivity (or equivalently with locally high Péclet numbers) o...

Countable systems of ordinary differential equations appear frequently in chemistry, physics, biology and statistics. They can be considered as ordinary differential equations in sequence spaces. In this work, a fully adaptive algorithm for the computational treatment of such systems is developed. The method is based on a time discretization of an abstract Cauchy problem in Hubert space and a d...

In this paper, we consider a discretization method proposed byWieners andWohlmuth [26] (see also [16]) for second order operators, which is a coupling between a mixed method in a sub-domain and a standard Galerkin method in the remaining part of the domain. We perform an a posteriori error analysis of residual type of this method, by combining some arguments from a posteriori error analysis of ...

We consider the space-time boundary element method (BEM) for heat equation with prescribed initial and Dirichlet data. propose a residual-type posteriori error estimator that is lower bound and, up to weighted $L_2$-norms of residual, also an upper unknown BEM error. The possibly locally refined meshes are assumed be prismatic, i.e., their elements tensor-products $J\times K$ in time $J$ space ...

We show that three well-known \variational crimes" in nite elements { upwinding, mass lumping and selective reduced integration { may be derived from the Galerkin method employing the standard polynomial-based nite element spaces enriched with residual-free bubbles.

Abstract. A new residual local projection stabilized method (RELP) is proposed as a result of an enriched Petrov-Galerkin strategy for the Oseen problem. The P 1 × Pl pairs, l = 0, 1 with continuous or discontinuous pressures, are made stable by enhancing them with solutions of residual-based local Oseen problems and performing a static condensation procedure afterward. This process does not in...

In the present study, the finite element method is developed for the static analysis of nano-beams under the Winkler foundation and the uniform load. The small scale effect along with Eringen's nonlocal elasticity theory is taken into account. The governing equations are derived based on the minimum potential energy principle. Galerkin weighted residual method is used to obtain the finite eleme...

An algorithm and essential subroutines programs are presented which implement two stage finite element Galerkin method for integrating the complete two dimensional horizontal flow model. In this method high accuracy is obtained by combining the Galerkin product with a high-order difference approximation to derivatives in the nonlinear advection operator. Program includes the use of a weighted s...

Abstract In this work, we are concerned with neural network guided goal-oriented a posteriori error estimation and adaptivity using the dual weighted residual method. The primal problem is solved classical Galerkin finite elements. adjoint in strong form feedforward two or three hidden layers. main objective of our approach to explore alternatives for solving greater potential numerical cost re...