Numerical analysis of a corrected Smagorinsky model [PDF]
Numerical Methods for Partial Differential Equations, 2022 The classical Smagorinsky model's solution is an approximation to a (resolved) mean velocity. Since it is an eddy viscosity model, it cannot represent a flow of energy from unresolved fluctuations to the (resolved) mean velocity.
Farjana Siddiqua, Xihui Xie
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Numerical analysis of a singularly perturbed convection diffusion problem with shift in space [PDF]
Applied Numerical Mathematics, 2022 We consider a singularly perturbed convection-diffusion problem that has in addition a shift term. We show a solution decomposition using asymptotic expansions and a stability result.
M. Brdar, S. Franz, L. Ludwig, H. Roos
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Numerical analysis of a finite volume scheme for charge transport in perovskite solar cells [PDF]
IMA Journal of Numerical Analysis, 2022 In this paper, we consider a drift-diffusion charge transport model for perovskite solar cells, where electrons and holes may diffuse linearly (Boltzmann approximation) or nonlinearly (e.g., due to Fermi–Dirac statistics).
Dilara Abdel +3 more
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An unfitted Eulerian finite element method for the time-dependent Stokes problem on moving domains [PDF]
IMA Journal of Numerical Analysis, 2020 We analyse a Eulerian finite element method, combining a Eulerian time-stepping scheme applied to the time-dependent Stokes equations with the CutFEM approach using inf-sup stable Taylor–Hood elements for the spatial discretization.
Henry von Wahl +2 more
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Optimally Convergent Mixed Finite Element Methods for the Stochastic Stokes Equations [PDF]
IMA Journal of Numerical Analysis, 2020 We propose some new mixed finite element methods for the time-dependent stochastic Stokes equations with multiplicative noise, which use the Helmholtz decomposition of the driving multiplicative noise. It is known (Langa, J. A., Real, J.
Xiaobing H. Feng, A. Prohl, Liet Vo
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A polynomial-degree-robust a posteriori error estimator for Nédélec discretizations of magnetostatic problems [PDF]
SIAM Journal on Numerical Analysis, 2020 We present an equilibration-based a posteriori error estimator for Nedelec element discretizations of the magnetostatic problem. The estimator is obtained by adding a gradient correction to the estimator for Nedelec elements of arbitrary degree presented
J. Gedicke +3 more
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Numerical analysis of a structure-preserving space-discretization for an anisotropic and heterogeneous boundary controlled N-dimensional wave equation as port-Hamiltonian system [PDF]
International Journal of Numerical Analysis and Modeling, 2020 The anisotropic and heterogeneous N-dimensional wave equation, controlled and observed at the boundary, is considered as a port-Hamiltonian system. The recent structure-preserving Partitioned Finite Element Method is applied, leading directly to a finite-
Ghislain Haine, D. Matignon, A. Serhani
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Numerical Analysis for Nematic Electrolytes [PDF]
IMA Journal of Numerical Analysis, 2020 We consider a system of nonlinear PDEs modeling nematic electrolytes, and construct a dissipative solution with the help of its implementable, structure-inheriting and space–time discretization.
L. Baňas, Robert Lasarzik, A. Prohl
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Variational and numerical analysis of a Q-tensor model for smectic-A liquid crystals [PDF]
ESAIM: Mathematical Modelling and Numerical Analysis, 2021 We analyse an energy minimisation problem recently proposed for modelling smectic-A liquid crystals. The optimality conditions give a coupled nonlinear system of partial differential equations, with a second-order equation for the tensor-valued nematic ...
Jingmin Xia, P. Farrell
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Mathematical modeling and numerical analysis for the higher order Boussinesq system [PDF]
ESAIM: Mathematical Modelling and Numerical Analysis, 2021 This study deals with higher-ordered asymptotic equations for the water-waves problem. We considered the higher-order/extended Boussinesq equations over a flat bottom topography in the well-known long wave regime. Providing an existence and uniqueness of
Bashar Bhorbatly +3 more
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