
Numerical solution for FokkerPlanck equation using a twolevel scheme
A numerical solution for the FokkerPlanck equation using a twolevel sc...
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An adaptive timestepping full discretization for stochastic AllenβCahn equation
It is known in [1] that a regular explicit Eulertype scheme with a unif...
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A postprocessing technique for a discontinuous Galerkin discretization of timedependent Maxwell's equations
We present a novel postprocessing technique for a discontinuous Galerkin...
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C^1conforming variational discretization of the biharmonic wave equation
Biharmonic wave equations are of importance to various applications incl...
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Semiexplicit discretization schemes for weaklycoupled ellipticparabolic problems
We prove firstorder convergence of the semiexplicit Euler scheme combi...
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Discrete Maximum principle of a high order finite difference scheme for a generalized AllenCahn equation
We consider solving a generalized AllenCahn equation coupled with a pas...
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An explicit and practically invariantspreserving method for conservative systems
An explicit numerical strategy that practically preserves invariants is ...
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Superconvergence of time invariants for the GrossPitaevskii equation
This paper considers the numerical treatment of the timedependent GrossPitaevskii equation. In order to conserve the time invariants of the equation as accurately as possible, we propose a CrankNicolsontype time discretization that is combined with a suitable generalized finite element discretization in space. The space discretization is based on the technique of Localized Orthogonal Decompositions (LOD) and allows to capture the time invariants with an accuracy of order πͺ(H^6) with respect to the chosen mesh size H. This accuracy is preserved due to the conservation properties of the time stepping method. Furthermore, we prove that the resulting scheme approximates the exact solution in the L^β(L^2)norm with order πͺ(Ο^2 + H^4), where Ο denotes the step size. The computational efficiency of the method is demonstrated in numerical experiments for a benchmark problem with known exact solution.
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