A collocation method of lines for two‐sided space‐fractional advection‐diffusion equations with variable coefficients
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DOI: 10.1002/mma.5592
Abstract: We present the Method Of Lines (MOL), which is based on the spectral collocation method, to solve space-fractional advection-diffusion equations (SFADEs) on a finite domain with variable coefficients. We focus on the cases in which… read more here.
Keywords: advection diffusion; collocation method; method;
The Crank‐Nicolson/interpolating stabilized element‐free Galerkin method to investigate the fractional Galilei invariant advection‐diffusion equation
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DOI: 10.1002/mma.5871
Abstract: Recently, finding a stable and convergent numerical procedure to simulate the fractional partial differential equations (PDEs) is one of the interesting topics. Meanwhile, the fractional advection‐diffusion equation is a challenge model numerically and analytically. This… read more here.
Keywords: advection diffusion; diffusion equation; fractional galilei;
New idea of Atangana‐Baleanu time‐fractional derivative to advection‐diffusion equation
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DOI: 10.1002/mma.6123
Abstract: The analytical study of one‐dimensional generalized fractional advection‐diffusion equation with a time‐dependent concentration source on the boundary is carried out. The generalization consists into considering the advection‐diffusion equation with memory based on the time‐fractional Atangana‐Baleanu… read more here.
Keywords: advection diffusion; diffusion equation; atangana baleanu; diffusion ... See more keywords
Asymptotic analysis of an advection‐diffusion equation involving interacting boundary and internal layers
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DOI: 10.1002/mma.6425
Abstract: As ε goes to zero, the unique solution of the scalar advection‐diffusion equation ytε−εyxxε+Myxε=0 , (x,t)∈(0,1)×(0,T) with Dirichlet boundary conditions exhibits a boundary layer of size O(ε) and an internal layer of size O(ε) .… read more here.
Keywords: advection diffusion; diffusion equation; asymptotic analysis;
Data completion problem for the advection‐diffusion equation with aquifer point sources
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DOI: 10.1002/mma.6868
Abstract: We consider the inverse problem of recovering the missing flux and concentration on some part of a boundary of an aquifer using overspecified measurements available on some accessible part. The aquifer is under the action… read more here.
Keywords: advection diffusion; point; diffusion equation; problem ... See more keywords
Evolution of dispersal in spatial population models with multiple timescales
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DOI: 10.1007/s00285-018-1302-2
Abstract: We study the evolutionary stability of dispersal strategies, including but not limited to those that can produce ideal free population distributions (that is, distributions where all individuals have equal fitness and there is no net… read more here.
Keywords: evolution; advection diffusion; population dynamics; evolution dispersal ... See more keywords
The effect of uncertain geometries on advection–diffusion of scalar quantities
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DOI: 10.1007/s10543-017-0676-7
Abstract: The two dimensional advection–diffusion equation in a stochastically varying geometry is considered. The varying domain is transformed into a fixed one and the numerical solution is computed using a high-order finite difference formulation on summation-by-parts… read more here.
Keywords: advection diffusion; geometries advection; geometry; effect uncertain ... See more keywords
Uniform Convergent Tailored Finite Point Method for Advection–Diffusion Equation with Discontinuous, Anisotropic and Vanishing Diffusivity
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DOI: 10.1007/s10915-016-0254-1
Abstract: We propose two tailored finite point methods for the advection–diffusion equation with anisotropic tensor diffusivity. The diffusion coefficient can be very small in one direction in some part of the domain and be discontinuous at… read more here.
Keywords: vanishing diffusivity; advection diffusion; diffusivity; tailored finite ... See more keywords
DPG Method with Optimal Test Functions for a Fractional Advection Diffusion Equation
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DOI: 10.1007/s10915-017-0369-z
Abstract: We develop an ultra-weak variational formulation of a fractional advection diffusion problem in one space dimension and prove its well-posedness. Based on this formulation, we define a DPG approximation with optimal test functions and show… read more here.
Keywords: optimal test; advection diffusion; fractional advection; test functions ... See more keywords
A Direct Flux Reconstruction Scheme for Advection–Diffusion Problems on Triangular Grids
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DOI: 10.1007/s10915-017-0472-1
Abstract: The direct flux reconstruction (DFR) scheme is a high-order numerical method which is an alternative realization of the flux reconstruction (FR) approach. In 1D, the DFR scheme has been shown to be equivalent to the… read more here.
Keywords: scheme; flux reconstruction; advection diffusion; direct flux ... See more keywords
Quartic-trigonometric tension B-spline Galerkin method for the solution of the advection-diffusion equation
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DOI: 10.1007/s40314-021-01526-2
Abstract: In this work, the numerical solutions of advection-diffusion equation are investigated through the finite element method. The quartic-trigonometric tension (QTT) B-spline which presents advantages over the well-known existing B-splines is adapted as the base of… read more here.
Keywords: quartic trigonometric; spline; method; equation ... See more keywords