# Theory of the Space-Time Discontinuous Galerkin Method for Nonstationary Parabolic Problems with Nonlinear Convection and Diffusion

@article{Cesenek2012TheoryOT, title={Theory of the Space-Time Discontinuous Galerkin Method for Nonstationary Parabolic Problems with Nonlinear Convection and Diffusion}, author={Jan Cesenek and Miloslav Feistauer}, journal={SIAM J. Numer. Anal.}, year={2012}, volume={50}, pages={1181-1206} }

The paper presents the theory of the space-time discontinuous Galerkin finite element method for the discretization of a nonstationary convection-diffusion initial-boundary value problem with nonlinear convection and nonlinear diffusion. The discontinuous Galerkin method is applied separately in space and time using, in general, different space grids on different time levels and different polynomial degrees p and q in space and time discretization. In the space discretization the nonsymmetric…

## 26 Citations

Stability of the ale space-time discontinuous Galerkin method for nonlinear convection-diffusion problems in time-dependent domains

- MathematicsESAIM: Mathematical Modelling and Numerical Analysis
- 2018

The paper is concerned with the analysis of the space-time discontinuous Galerkin method (STDGM) applied to the numerical solution of nonstationary nonlinear convection-diffusion initial- boundary…

On the stability of the ale space-time discontinuous Galerkin method for nonlinear convection-diffusion problems in time-dependent domains

- Computer Science
- 2015

The analysis of the space-time discontinuous Galerkin method applied to the numerical solution of the nonstationary nonlinear convection-diffusion initial-boundary value problem in a time-dependent domain formulated with the aid of the arbitrary Lagrangian-Eulerian method.

Stability analysis of the space-time discontinuous Galerkin method for nonstationary nonlinear convection-diffusion problems

- Computer Science
- 2015

This paper is concerned with the stability analysis of the space-time discontinuous Galerkin method for the solution of nonstationary, nonlinear, convection-diffusion problems. In the formulation of…

Analysis of Space-Time DGFEM for the Solution of Nonstationary Nonlinear Convection-Diffusion Problems

- Computer ScienceENUMATH
- 2013

The main attention is paid to the investigation of unconditional stability of the Galerkin method, and an important tool is the concept of the discrete characteristic function.

Discontinuous Galerkin method in time combined with a stabilized finite element method in space for linear first-order PDEs

- Computer Science, MathematicsMath. Comput.
- 2016

The discontinuous Galerkin method in time combined with a finite element method with symmetric stabilization in space to approximate evolution problems with a linear, first-order differential operator and new optimal bounds on static meshes for the error in the time-derivative and in the discrete graph norm are proved.

Error analysis for discretizations of parabolic problems using continuous finite elements in time and mixed finite elements in space

- Mathematics, Computer ScienceNumerische Mathematik
- 2017

A family of continuous Galerkin–Petrov time discretization schemes that is combined with a mixed finite element approximation of the spatial variables are considered, and the existence and uniqueness of the semidiscrete approximation and of the fully discrete solution are established.

Full-Discrete Weak Galerkin Finite Element Method for Solving Diffusion-Convection Problem.

- Mathematics
- 2017

This paper applied and analyzes full discrete weak Galerkin (WG) finite element method for non steady two dimensional convection-diffusion problem on conforming polygon. We approximate the time…

Unified error analysis of discontinuous Galerkin methods for parabolic obstacle problem

- Computer Science, Mathematics
- 2021

A unified error analysis for all well known symmetric and non-symmetric DG fully discrete schemes is presented, and error estimate of optimal order is derived in an energy norm.

Space-time discontinuous Galerkin method for the solution of fluid-structure interaction

- EngineeringApplications of Mathematics
- 2018

The paper is concerned with the application of the space-time discontinuous Galerkin method (STDGM) to the numerical solution of the interaction of a compressible flow and an elastic structure. The…

A space-time discontinuous Galerkin method for Boussinesq-type equations

- Mathematics, Computer ScienceAppl. Math. Comput.
- 2016

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