Linearly Implicit IMEX Runge--Kutta Methods for a Class of Degenerate Convection-Diffusion Problems

2015 ◽  
Vol 37 (2) ◽  
pp. B305-B331 ◽  
Author(s):  
Sebastiano Boscarino ◽  
Raimund Bürger ◽  
Pep Mulet ◽  
Giovanni Russo ◽  
Luis M. Villada
Keyword(s):  
Convection Diffusion ◽  
Runge Kutta ◽  
Diffusion Problems

On linearly implicit IMEX Runge-Kutta methods for degenerate convection-diffusion problems modeling polydisperse sedimentation

2016 ◽  
Vol 47 (1) ◽  
pp. 171-185 ◽  
Author(s):  
Sebastiano Boscarino ◽  
Raimund Bürger ◽  
Pep Mulet ◽  
Giovanni Russo ◽  
Luis Miguel Villada
Keyword(s):  
Convection Diffusion ◽  
Runge Kutta ◽  
Diffusion Problems

Error estimates of the third order runge-kutta alternating evolution discontinuous galerkin method for convection-diffusion problems

2018 ◽  
Vol 52 (5) ◽  
pp. 1709-1732
Author(s):  
Hailiang Liu ◽  
Hairui Wen
Keyword(s):  
Stability Analysis ◽  
Error Estimates ◽  
Discontinuous Galerkin ◽  
Energy Estimates ◽  
Third Order ◽  
Convection Diffusion ◽  
Temporal Discretization ◽  
Runge Kutta ◽  
The Stability ◽  
Diffusion Problems

In this paper, we present the stability analysis and error estimates for the alternating evolution discontinuous Galerkin (AEDG) method with third order explicit Runge-Kutta temporal discretization for linear convection-diffusion equations. The scheme is shown stable under a CFL-like stability condition c0τ ≤ ε ≤ c1h2. Here ε is the method parameter, and h is the maximum spatial grid size. We further obtain the optimal L2 error of order O(τ3 + hk+1). Key tools include two approximation finite element spaces to distinguish overlapping polynomials, coupled global projections, and energy estimates of errors. For completeness, the stability analysis and error estimates for second order explicit Runge-Kutta temporal discretization is included in the appendix.

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