Displaying similar documents to “On the stability of the ALE space-time discontinuous Galerkin method for nonlinear convection-diffusion problems in time-dependent domains”

Analysis of the discontinuous Galerkin finite element method applied to a scalar nonlinear convection-diffusion equation

Hozman, Jiří, Dolejší, Vít

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We deal with a scalar nonstationary convection-diffusion equation with nonlinear convective as well as diffusive terms which represents a model problem for the solution of the system of the compressible Navier-Stokes equations describing a motion of viscous compressible fluids. We present a discretization of this model equation by the discontinuous Galerkin finite element method. Moreover, under some assumptions on the nonlinear terms, domain partitions and the regularity of the exact...

An adaptive h p -discontinuous Galerkin approach for nonlinear convection-diffusion problems

Dolejší, Vít

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We deal with a numerical solution of nonlinear convection-diffusion equations with the aid of the discontinuous Galerkin method (DGM). We propose a new h p -adaptation technique, which is based on a combination of a residuum estimator and a regularity indicator. The residuum estimator as well as the regularity indicator are easily evaluated quantities without the necessity to solve any local problem and/or any reconstruction of the approximate solution. The performance of the proposed h p -DGM...

Global existence and stability of solution for a nonlinear Kirchhoff type reaction-diffusion equation with variable exponents

Aya Khaldi, Amar Ouaoua, Messaoud Maouni (2022)

Mathematica Bohemica

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We consider a class of Kirchhoff type reaction-diffusion equations with variable exponents and source terms u t - M ∫ Ω | ∇ u | 2 d x Δ u + | u | m ( x ) - 2 u t = | u | r ( x ) - 2 u . We prove with suitable assumptions on the variable exponents r ( · ) , m ( · ) the global existence of the solution and a stability result using potential and Nihari’s functionals with small positive initial energy, the stability being based on Komornik’s inequality.

Remarks on balanced norm error estimates for systems of reaction-diffusion equations

Hans-Goerg Roos (2018)

Applications of Mathematics

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Error estimates of finite element methods for reaction-diffusion problems are often realized in the related energy norm. In the singularly perturbed case, however, this norm is not adequate. A different scaling of the H 1 seminorm leads to a balanced norm which reflects the layer behavior correctly. We discuss the difficulties which arise for systems of reaction-diffusion problems.

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

Balázsová, Monika, Feistauer, Miloslav, Hadrava, Martin, Kosík, Adam

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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 the numerical scheme we use the nonsymmetric, symmetric and incomplete versions of the discretization of diffusion terms and interior and boundary penalty. Then error estimates are briefly characterized. The main attention is paid to the investigation of unconditional stability of the method....

A well-posedness result for a mass conserved Allen-Cahn equation with nonlinear diffusion

Kettani, Perla El, Hilhorst, Danielle, Lee, Kai

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In this paper, we prove the existence and uniqueness of the solution of the initial boundary value problem for a stochastic mass conserved Allen-Cahn equation with nonlinear diffusion together with a homogeneous Neumann boundary condition in an open bounded domain of ℝ n with a smooth boundary. We suppose that the additive noise is induced by a Q-Brownian motion.