This paper develops a high-order adaptive scheme for solving nonlinear Schrödinger equations. The solutions to such equations often exhibit solitary wave and local structures, which make adaptivity essential in improving the simulation efficiency. Our uses ultra-weak discontinuous Galerkin (DG) formulation belongs framework of multiresolution schemes. Various numerical experiments are presented...

An adaptive modified weak Galerkin method (AmWG) for an elliptic problem is studied in this paper, addition to its convergence and optimality. The bilinear form simplified without the need of skeletal variable, approximation space chosen as discontinuous polynomial method. Upon a reliable residual-based posteriori error estimator, algorithm proposed together with quasi-optimality proved lowest ...

In this paper, we propose a new numerical scheme for the coupled Stokes-Darcy model with Beavers-Joseph-Saffman interface condition. We use weak Galerkin method to discretize Stokes equation and mixed finite element Darcy equation. A discrete inf-sup condition is proved optimal error estimates are also derived. Numerical experiments validate theoretical analysis.

In this paper, our purpose is to study the classical continuous optimal control (CCOC) for quaternary nonlinear parabolic boundary value problems (QNLPBVPs). The existence and uniqueness theorem (EUTh) state vector solution (QSVS) of weak form (WF) QNLPBVPs with a given (QCCCV) stated proved via Galerkin Method (GM) first compactness under suitable assumptions(ASSUMS). Furthermore, continuity o...

The essential features of the Meshless Local Petrov-Galerkin (MLPG) method, and of the Local Boundary Integral Equation (LBIE) method, are critically examined from the points of view of a non-element interpolation of the ®eld variables, and of the meshless numerical integration of the weak form to generate the stiffness matrix. As truly meshless methods, the MLPG and the LBIE methods hold a gre...

In this paper, we consider two dimensional nonlinear elliptic equations of the form $ -{rm div}(a(u,nabla u)) = f $. Then, in order to solve these equations on rectangular domains, we propose a numerical method based on Sinc-Galerkin method. Finally, the presented method is tested on some examples. Numerical results show the accuracy and reliability of the proposed method.

Abstract. The present paper introduces bilinear forms that are equivalent to the recovery-based discontinuous Galerkin formulation introduced by Van Leer in 2005. The recovery method approximates the solution of the diffusion equation in a discontinuous function space, while inter-element coupling is achieved by a local L2 projection that recovers a smooth continuous function underlying the dis...