Displaying similar documents to “Implicit-explicit Runge–Kutta schemes and finite elements with symmetric stabilization for advection-diffusion equations”

Implicit-explicit Runge–Kutta schemes and finite elements with symmetric stabilization for advection-diffusion equations

Erik Burman, Alexandre Ern (2012)

ESAIM: Mathematical Modelling and Numerical Analysis

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We analyze a two-stage implicit-explicit Runge–Kutta scheme for time discretization of advection-diffusion equations. Space discretization uses continuous, piecewise affine finite elements with interelement gradient jump penalty; discontinuous Galerkin methods can be considered as well. The advective and stabilization operators are treated explicitly, whereas the diffusion operator is treated implicitly. Our analysis hinges on -energy estimates on discrete functions in...

Implicit-explicit Runge–Kutta schemes and finite elements with symmetric stabilization for advection-diffusion equations

Erik Burman, Alexandre Ern (2012)

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique

Similarity:

We analyze a two-stage implicit-explicit Runge–Kutta scheme for time discretization of advection-diffusion equations. Space discretization uses continuous, piecewise affine finite elements with interelement gradient jump penalty; discontinuous Galerkin methods can be considered as well. The advective and stabilization operators are treated explicitly, whereas the diffusion operator is treated implicitly. Our analysis hinges on -energy estimates on discrete functions in...

Time discretizations for evolution problems

Miloslav Vlasák (2017)

Applications of Mathematics

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The aim of this work is to give an introductory survey on time discretizations for liner parabolic problems. The theory of stability for stiff ordinary differential equations is explained on this problem and applied to Runge-Kutta and multi-step discretizations. Moreover, a natural connection between Galerkin time discretizations and Runge-Kutta methods together with order reduction phenomenon is discussed.