Discontinuous Galerkin framework for adaptive solution of parabolic problems

2007 ◽  
Vol 70 (1) ◽  
pp. 1-24 ◽  
Author(s):  
Deepak V. Kulkarni ◽  
Dimitrios V. Rovas ◽  
Daniel A. Tortorelli
Keyword(s):  
Discontinuous Galerkin ◽  
Parabolic Problems ◽  
Adaptive Solution

scholarly journals A splitting mixed space-time discontinuous Galerkin method for parabolic problems

2012 ◽  
Vol 31 ◽  
pp. 1050-1059 ◽  
Author(s):  
Siriguleng He ◽  
Hong Li ◽  
Yang Liu ◽  
Zhichao Fang ◽  
Jingbo Yang ◽  
...  
Keyword(s):  
Galerkin Method ◽  
Discontinuous Galerkin ◽  
Discontinuous Galerkin Method ◽  
Space Time ◽  
Parabolic Problems

scholarly journals A Review of Residual Distribution Schemes for Hyperbolic and Parabolic Problems: The July 2010 State of the Art

2012 ◽  
Vol 11 (4) ◽  
pp. 1043-1080 ◽  
Author(s):  
Remi Abgrall
Keyword(s):  
Finite Element ◽  
Discontinuous Galerkin ◽  
State Of The Art ◽  
Natural Extension ◽  
Parabolic Problems ◽  
Residual Distribution ◽  
Finite Volume Schemes ◽  
Stabilized Finite Element ◽  
Research Perspectives ◽  
Residual Distribution Schemes

AbstractWe describe and review non oscillatory residual distribution schemes that are rather natural extension of high order finite volume schemes when a special emphasis is put on the structure of the computational stencil. We provide their connections with standard stabilized finite element and discontinuous Galerkin schemes, show that their are really non oscillatory. We also discuss the extension to these methods to parabolic problems. We also draw some research perspectives.

scholarly journals Discontinuous Galerkin time discretization methods for parabolic problems with linear constraints

2019 ◽  
Vol 27 (3) ◽  
pp. 155-182 ◽  
Author(s):  
Igor Voulis ◽  
Arnold Reusken
Keyword(s):  
Discontinuous Galerkin ◽  
Error Bounds ◽  
Convergence Rates ◽  
Time Discretization ◽  
Linear Constraints ◽  
Dirichlet Boundary Conditions ◽  
Time Dependent ◽  
Parabolic Problems ◽  
Discretization Methods ◽  
Optimal Convergence

Abstract We consider time discretization methods for abstract parabolic problems with inhomogeneous linear constraints. Prototype examples that fit into the general framework are the heat equation with inhomogeneous (time-dependent) Dirichlet boundary conditions and the time-dependent Stokes equation with an inhomogeneous divergence constraint. Two common ways of treating such linear constraints, namely explicit or implicit (via Lagrange multipliers) are studied. These different treatments lead to different variational formulations of the parabolic problem. For these formulations we introduce a modification of the standard discontinuous Galerkin (DG) time discretization method in which an appropriate projection is used in the discretization of the constraint. For these discretizations (optimal) error bounds, including superconvergence results, are derived. Discretization error bounds for the Lagrange multiplier are presented. Results of experiments confirm the theoretically predicted optimal convergence rates and show that without the modification the (standard) DG method has sub-optimal convergence behavior.

scholarly journals hp-Discontinuous Galerkin time stepping for parabolic problems

2001 ◽  
Vol 190 (49-50) ◽  
pp. 6685-6708 ◽  
Author(s):  
T. Werder ◽  
K. Gerdes ◽  
D. Schötzau ◽  
C. Schwab
Keyword(s):  
Discontinuous Galerkin ◽  
Parabolic Problems ◽  
Time Stepping
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