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

DOI10.1007/s10492-015-0109-3zbMath1363.65157OpenAlexW1690711049MaRDI QIDQ499037

Miloslav Feistauer, Monika Balázsová

Publication date: 29 September 2015

Published in: Applications of Mathematics (Search for Journal in Brave)

Full work available at URL: http://hdl.handle.net/10338.dmlcz/144389

zbMATH Keywords

initial-boundary value problemunconditional stabilityspace-time discontinuous Galerkin methodtime-dependent domainLagrangian-Eulerian methodnonstationary nonlinear convection-diffusion equations

Mathematics Subject Classification ID

Nonlinear parabolic equations (35K55) Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs (65M12) Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs (65M60)

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Cites Work

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• Discontinuous Galerkin method for nonlinear convection-diffusion problems with mixed Dirichlet-Neumann boundary conditions
• Analysis of space-time discontinuous Galerkin method for nonlinear convection-diffusion problems
• A high-order accurate discontinuous finite element method for the numerical solution of the compressible Navier-Stokes equations
• On the stability of the space-time discontinuous Galerkin method for the numerical solution of nonstationary nonlinear convection-diffusion problems
• Space-time discontinuous Galerkin method for solving nonstationary convection-diffusion-reaction problems.
• Discontinuous Galerkin solution of compressible flow in time-dependent domains
• A discontinuous \(hp\) finite element method for diffusion problems
• Abstract of the PhD thesis: ``\(hp\)-DGFEM for parabolic evolution problems -- applications to diffusion and viscous incompressible fluid flow
• Runge--Kutta discontinuous Galerkin methods for convection-dominated problems
• An arbitrary Lagrangian-Eulerian finite element method for transient dynamic fluid-structure interactions
• An \(hp\) a priori error analysis of the DG time-stepping for initial value problems
• A discontinuous \(hp\) finite element method for diffusion problems: 1-D analysis
• DGFEM for dynamical systems describing interaction of compressible fluid and structures
• Analysis of semi-implicit DGFEM for nonlinear convection-diffusion problems on nonconforming meshes
• Simulation of compressible viscous flow in time-dependent domains
• DGFEM for the analysis of airfoil vibrations induced by compressible flow
• Theory of the Space-Time Discontinuous Galerkin Method for Nonstationary Parabolic Problems with Nonlinear Convection and Diffusion
• Adaptive Finite Element Methods for Parabolic Problems I: A Linear Model Problem
• The discontinuous Galerkin method for semilinear parabolic problems
• Unified Analysis of Discontinuous Galerkin Methods for Elliptic Problems
• Discontinuoushp-Finite Element Methods for Advection-Diffusion-Reaction Problems
• On the discontinuous Galerkin method for the numerical solution of the Navier–Stokes equations
• Time-Discrete Higher-Order ALE Formulations: Stability
• Discontinuous Galerkin Method
• Galerkin time-stepping methods for nonlinear parabolic equations
• NUMERICAL STABILITY OF THE FINITE ELEMENT IMMERSED BOUNDARY METHOD
• Error Estimates for the Discontinuous Galerkin Methods for Parabolic Equations
• Galerkin Finite Element Methods for Parabolic Problems