scholarly journals Error Analysis of Nitsche’s and Discontinuous Galerkin Methods of a Reduced Landau–de Gennes Problem

2020 ◽  
Vol 0 (0) ◽  
Author(s):  
Ruma Rani Maity ◽  
Apala Majumdar ◽  
Neela Nataraj
Keyword(s):  
Discontinuous Galerkin ◽  
Nonlinear Term ◽  
A Priori ◽  
Dirichlet Boundary Conditions ◽  
Galerkin Methods ◽  
Liquid Crystal Devices ◽  
Priori Error Estimates ◽  
Posteriori Analysis ◽  
Theoretical Results ◽  
A Posteriori Analysis

AbstractWe study a system of semi-linear elliptic partial differential equations with a lower order cubic nonlinear term, and inhomogeneous Dirichlet boundary conditions, relevant for two-dimensional bistable liquid crystal devices, within a reduced Landau–de Gennes framework. The main results are (i) a priori error estimates for the energy norm, within the Nitsche’s and discontinuous Galerkin frameworks under milder regularity assumptions on the exact solution and (ii) a reliable and efficient a posteriori analysis for a sufficiently large penalization parameter and a sufficiently fine triangulation in both cases. Numerical examples that validate the theoretical results, are presented separately.

Penalty-free discontinuous Galerkin methods for incompressible Navier–Stokes equations

2014 ◽  
Vol 24 (06) ◽  
pp. 1217-1236 ◽  
Author(s):  
Beatrice Riviere ◽  
Shirin Sardar
Keyword(s):  
Discontinuous Galerkin ◽  
Discontinuous Galerkin Methods ◽  
Stokes Equations ◽  
A Priori ◽  
Navier Stokes ◽  
Galerkin Methods ◽  
Navier Stokes Equations ◽  
First Order ◽  
Priori Error Estimates ◽  
The Stability

A first-order discontinuous Galerkin method is proposed for solving the steady-state incompressible Navier–Stokes equations. The stability of this penalty-free method is obtained by locally enriching the discrete space with a quadratic polynomial. A priori error estimates are derived. Numerical examples confirm the theoretical convergence.

scholarly journals Stable Filtering Procedures for Nodal Discontinuous Galerkin Methods

2021 ◽  
Vol 87 (1) ◽  
Author(s):  
Jan Nordström ◽  
Andrew R. Winters
Keyword(s):  
Discontinuous Galerkin ◽  
Discontinuous Galerkin Methods ◽  
Finite Difference Methods ◽  
Basis Functions ◽  
Galerkin Methods ◽  
Theoretical Discussion ◽  
Numerical Tests ◽  
Dg Methods ◽  
Theoretical Results ◽  
Filtering Procedure

AbstractWe prove that the most common filtering procedure for nodal discontinuous Galerkin (DG) methods is stable. The proof exploits that the DG approximation is constructed from polynomial basis functions and that integrals are approximated with high-order accurate Legendre–Gauss–Lobatto quadrature. The theoretical discussion re-contextualizes stable filtering results for finite difference methods into the DG setting. Numerical tests verify and validate the underlying theoretical results.

scholarly journals A priori and a posteriori analysis of the flow around a rectangular cylinder

2017 ◽  
Vol 923 ◽  
pp. 012028
Author(s):  
A Cimarelli ◽  
A Leonforte ◽  
M Franciolini ◽  
E De Angelis ◽  
D Angeli ◽  
...  
Keyword(s):  
A Priori ◽  
A Posteriori ◽  
Rectangular Cylinder ◽  
Posteriori Analysis ◽  
A Posteriori Analysis
Sign in / Sign up

Export Citation Format

Share Document