A new symmetric local projection method built on residual bases (RELP) makes linear equal-order finite element pairs stable for the Darcy problem. The derivation is performed inside a Petrov-Galerkin enriching space approach (PGEM) which indicates parameter-free terms to be added to the Galerkin method without compromising consistency. Velocity and pressure spaces are augmented using solutions ...

In this paper, static and dynamic behavior of a varactor of a micro-phase shifter under DC, step DC and AC voltages and effects of the residual stress on the phase diagram have been studied. By presenting a mathematical modeling, Galerkin-based step by step linearization method (SSLM) and Galerkin-based reduced order model have been used to solve the governing static and dynamic equations, resp...

We propose and analyze a posteriori energy-norm error estimates for weighted interior penalty discontinuous Galerkin approximations of advection-diffusion-reaction equations with heterogeneous and anisotropic diffusion. The weights, which play a key role in the analysis, depend on the diffusion tensor and are used to formulate the consistency terms in the discontinuous Galerkin method. The erro...

Abstract In this study, a novel method for improving the simulation of wave propagation in Peridynamic (PD) media is investigated. Initially, dispersion properties nonlocal Bond-Based model are computed 1-D and 2-D uniform grids. The optimization problem, developed through inverse analysis, set up by comparing exact numerical minimizing error. Various weighted residual techniques, i.e., point c...

A robust multilevel preconditioner based on the hybridizable discontinuous Galerkin method for the Helmholtz equation with high wave number is presented in this paper. There are two keys in our algorithm, one is how to choose a suitable intergrid transfer operator, and the other is using GMRES smoothing on coarse grids. The multilevel method is performed as a preconditioner in the outer GMRES i...

In this paper, a space-time finite element method based on Galerkin-weighted residual is proposed to solve the nonlinear fully intrinsic equations of geometrically exact beam which are first-order partial differential about time and space. Therefore, it natural discretize in space simultaneously. Considering continuity boundary conditions spatial direction periodic direction, value scheme for s...

The numerical simulation of complex physical processes requires the use of economical discrete models. This lecture presents a general paradigm of deriving a posteriori error estimates for the Galerkin finite element approximation of nonlinear problems. Employing duality techniques as used in optimal control theory the error in the target quantities is estimated in terms of weighted ‘primal’ an...

We present a space-time certified reduced basis method for long-time integration of parametrized noncoercive parabolic equations with quadratic nonlinearity. We first consider a finite element discretization based on discontinuous Galerkin time integration and introduce associated Petrov-Galerkin space-time trialand test-space norms which yields optimal and asymptotically mesh independent stabi...

We present a novel approach to the simulation of miscible displacement by employing adaptive enriched Galerkin finite element methods (EG) coupled with entropy residual stabilization for transport. In particular, numerical simulations of viscous fingering instabilities in heterogeneous porous media and Hele-Shaw cells are illustrated. EG is formulated by enriching the conforming continuous Gale...

In this paper we present two different kinds of error estimators for acoustic problems: a residual-based and a dual weighted residual one. The former error estimator is explicit and cheap to compute. The latter is based on a duality argument and it is capable of computing accurate and reliable estimations of quantities of interest, which can be safely used for finite element analysis and model ...