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Finite element analysis of an arbitrary Lagrangian–Eulerian method for Stokes/parabolic moving interface problem with jump coefficients [PDF]
Results in Applied Mathematics, 2020 In this paper, a type of arbitrary Lagrangian–Eulerian (ALE) finite element method in the monolithic frame is developed for a linearized fluid–structure interaction (FSI) problem — an unsteady Stokes/parabolic interface problem with jump coefficients and
Rihui Lan +2 more
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Computation, 2021 The matched interface and boundary method (MIB) and ghost fluid method (GFM) are two well-known methods for solving elliptic interface problems. Moreover, they can be coupled with efficient time advancing methods, such as the alternating direction ...
Chuan Li +3 more
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Journal of Computational and Applied Mathematics, 2021 This article discusses a monolithic arbitrary Lagrangian-Eulerian (ALE) finite element method. A stable Stokes-pair mixed finite element within a specific stabilization technique and a novel ALE time-difference scheme are developed to discretize this interface problem in both semi-discrete and fully discrete fashion, for which the stability and error ...
Rihui Lan, Pengtao Sun
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The Immersed Interface Technique for Parabolic Problems with Mixed Boundary Conditions [PDF]
SIAM Journal on Numerical Analysis, 2010 A finite difference scheme is presented for a parabolic problem with mixed boundary conditions. We use an immersed interface technique to discretize the Neumann condition, and we use the Shortley-Weller approximation for the Dirichlet condition. The proof of a discrete maximum principle is given as well as the proof of convergence of the scheme.
Bouchon, François, Peichl, Gunther
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IMA Journal of Numerical AnalysisAbstract We consider a parabolic–parabolic interface problem and construct a loosely coupled prediction-correction scheme based on the Robin–Robin splitting method analyzed in [J. Numer. Math., 31(1):59–77, 2023]. We show that the errors of the correction step converge at $\mathcal O((\varDelta t)^{2})$, under suitable convergence ...
Erik Burman +2 more
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Construction of a numerical model and algorithm for solving two-dimensional problems of filtration of multicomponent liquids, taking into account the moving “oil-water” interface [PDF]
E3S Web of Conferences, 2023 The paper considers a two-dimensional mathematical model of the filtration of a viscous, incompressible fluid in a deformable porous medium. The article describes a mathematical model of the problem at the “oil-water” interface with a system of parabolic
Nazirova E. Sh. +3 more
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A screw dislocation located outside, inside or on the interface of a parabolic elastic inhomogeneity
Archives of Mechanics, 2021 Using conformal mapping techniques, superposition and analytic continuation, we derive analytic solutions to the problem of a screw dislocation interacting with a parabolic elastic inhomogeneity.
X. Wang, P. Schiavone
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Multisector Parabolic Equation Method for Scattering From Impenetrable Objects in Fluid Waveguides
IEEE Access, 2021 Parabolic equation methods are a robust and efficient tool for modeling long-range acoustic propagation in range-dependent waveguides. A lesser known, but equally effective, application of parabolic equations is to the scattering problem.
Adith Ramamurti, David C. Calvo
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Computation, 2023 The paper is devoted to the theoretical analysis and numerical implementation of a mathematical model of a nonlinear reaction–diffusion system on the COMSOL Multiphysics platform.
Elena Veselova +2 more
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Numerical Solution of the Retrospective Inverse Parabolic Problem on Disjoint Intervals
Computation, 2023 The retrospective inverse problem for evolution equations is formulated as the reconstruction of unknown initial data by a given solution at the final time.
Miglena N. Koleva, Lubin G. Vulkov
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