We consider an evolutionary problem with rapidly oscillating coefficients. This causes the problem to change frequently between a parabolic and a hyperbolic state. We prove convergence of the homogenisation process in...
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In this paper we deal with the efficient resolution of a coupled system of two one dimensional, time dependent, semilinear parabolic singularly perturbed partial differential equations of reaction-diffusion type, with...
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Algebraic flux correction (AFC) finite element discretizations of steady-state convection-diffusion-reaction equations lead to a nonlinear problem. This paper presents first steps of a systematic study of solvers for ...
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Consider the transient incompressible Navier-Stokes flow at high Reynolds numbers. A high-order H(div)-conforming FEM with pointwise divergence-free discrete velocities is applied to implicit large-eddy-simulation in ...
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Even though substantial progress has been made in the numerical approximation of convection-dominated problems, its major challenges remain in the scope of current research by John et al. (Comput Vis Sci 19(5–6):1–1...
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We construct and analyze implicit–explicit multistep schemes for nonlinear evolution convection–diffusion partial differential equations. We establish optimal order a priori error estimates. We are particularly inte...
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The importance of H(div)-conforming approximations is well recognized for conservative mixed formulations of multiphysics systems. There exists in the literature a variety of such approximation spaces, which are usual...
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In the recent article (Kopteva, Numer Math 137:607–642, 2017) the author obtained residual-type a posteriori error estimates in the energy norm for singularly perturbed semilinear reaction-diffusion equations on unst...
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