Adaptive finite element methods for parabolic problems IV: nonlinear problems
SIAM Journal on Numerical Analysis
A convergent adaptive algorithm for Poisson's equation
SIAM Journal on Numerical Analysis
Finite Element Method for Elliptic Problems
Finite Element Method for Elliptic Problems
An Implicit-Explicit Runge--Kutta--Chebyshev Scheme for Diffusion-Reaction Equations
SIAM Journal on Scientific Computing
RKC time-stepping for advection-diffusion-reaction problems
Journal of Computational Physics
Journal of Scientific Computing
Entropy/energy stable schemes for evolutionary dispersal models
Journal of Computational Physics
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We introduce in this paper an adaptive method that combines a semi-Lagrangian scheme with a second order implicit-explicit Runge-Kutta-Chebyshev (IMEX RKC) method to calculate the numerical solution of convection dominated reaction-diffusion problems in which the reaction terms are highly stiff. The convection terms are integrated via the semi-Lagrangian scheme, whereas the IMEX RKC treats the diffusion terms explicitly and the highly stiff reaction terms implicitly. The space adaptation is done in the framework of finite elements and the criterion for adaptation is derived from the information supplied by the semi-Lagrangian step; so that, this can be considered a heuristic approach to adaptivity that is somewhat similar to the so-called r-adaptivity strategy.