A framework is presented for step-by-step implementation of weighted-residual methods (MWR) for simulations that require the solution of boundary-value problems. A set of Matlab-based functions of the computationally common MWR solution steps has been developed and is used in the application of eigenfunction expansion, collocation, and Galerkin-projection discretizations of time-dependent, dist...

In this paper the meshless local Petrov-Galerkin (MLPG) method is implemented to study the buckling of isotropic cylindrical shells under axial load. Displacement field equations, based on Donnell and first order shear deformation theory, are taken into consideration. The set of governing equations of motion are numerically solved by the MLPG method in which according to a semi-inverse method, ...

We present a residual based artificial viscosity finite element method to solve conservation laws. The Galerkin approximation is stabilized by only residual based artificial viscosity, without any least-squares, SUPG, or streamline diffusion terms. We prove convergence of the method, applied to a scalar conservation law in two space dimensions, toward an unique entropy solution for implicit tim...

A new interface treating method is proposed to simulate compressible two-medium problems with the Runge-Kutta discontinuous Galerkin (RKDG) method. In present work, both Euler equation and level-set are discretized RKDG which compact of high-order accuracy. The linearized inside an cell recovered by function. solution this taken as a convex combination two auxiliary solutions. One obtained for ...

A novel iteration scheme, using boundary integral equations, is developed for error estimation in the boundary element method. The iteration scheme consists of using the boundary integral equation for solving the boundary value problem and iterating this solution with the hypersingular boundary integral equation to obtain a new solution. The hypersingular residual r is consistently defined as t...

In this paper, we introduce the isoGeometric Residual Minimization (iGRM) method. The method solves stationary advection-dominated diffusion problems. We stabilize via residual minimization. discretize problem using B-spline basis functions. then seek to minimize isogeometric over a spline space built on tensor product mesh. construct solution smooth subspace of residual. can specify by reducin...

Abstract This paper presents a multirate in time approach for coupled flow and transport problems combined with goal-oriented error control based on the Dual Weighted Residual (DWR) method. The focus is implementation of concept regarding different scales underlying subproblems. Key ingredients are an arbitrary degree discontinuous Galerkin discretization, posteriori representation problem spac...

One-dimensional convection-diffusion problem with interior layers caused by the discontinuity of data is considered. Though standard Galerkin finite element method (FEM) generates oscillations in the numerical solutions, we prove its convergence in the ε-weighted norm of the first order on a class of layer-adapted meshes. We use streamline-diffusion finite element method (SDFEM) in order to sta...