Parameter‐robust higher‐order time‐accurate computational method for singularly perturbed time‐dependent semilinear convection‐diffusion PDEs with discontinuous data
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DOI: 10.1002/mma.10070
Abstract: This article is concerned with a class of singularly perturbed semilinear parabolic convection‐diffusion partial differential equations (PDEs) with discontinuous source function. Solutions of these PDEs usually exhibit a weak interior layer at one side of… read more here.
Keywords: singularly perturbed; method; time; solution ... See more keywords
Unisolvence of Randomized MultiQuadric Kansa Collocation for Convection–Diffusion with Mixed Boundary Conditions
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DOI: 10.1007/s00009-025-02918-y
Abstract: We make a further step in the open problem of unisolvence for unsymmetric Kansa collocation, proving that the MultiQuadric Kansa method with fixed collocation points and random fictitious centers is almost surely unisolvent, for stationary… read more here.
Keywords: collocation; mixed boundary; multiquadric kansa; convection diffusion ... See more keywords
Analysis of direct discontinuous Galerkin methods for multi-dimensional convection-diffusion equations
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DOI: 10.1007/s00211-021-01183-x
Abstract: We provide a framework for the analysis of the direct discontinuous Galerkin (DDG) methods for multi-dimensional convection-diffusion equations subject to various boundary conditions. A key tool is the global projection constructed by the DDG scheme… read more here.
Keywords: analysis direct; convection diffusion; discontinuous galerkin; direct discontinuous ... See more keywords
Virtual element method stabilization for convection-diffusion-reaction problems using the link-cutting condition
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DOI: 10.1007/s10092-016-0180-5
Abstract: In this paper, we present a methodology for stabilizing the virtual element method applied to the convection-diffusion-reaction equation. The stabilization is carried out modifying the mesh inside the boundary layer so that the link-cutting condition… read more here.
Keywords: convection diffusion; element method; diffusion reaction; link cutting ... See more keywords
A posteriori error estimates for non-stationary non-linear convection–diffusion equations
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DOI: 10.1007/s10092-018-0263-6
Abstract: Motivated by stochastic convection–diffusion problems we derive a posteriori error estimates for non-stationary non-linear convection–diffusion equations acting as a deterministic paradigm. The problem considered here neither fits into the standard linear framework due to its… read more here.
Keywords: convection diffusion; diffusion; convection; non linear ... See more keywords
Analysis of local discontinuous Galerkin method for time–space fractional convection–diffusion equations
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DOI: 10.1007/s10543-018-0697-x
Abstract: This paper focuses on the time–space fractional convection–diffusion equations with time fractional derivative (of order $$\alpha $$α, $$0< \alpha read more here.
Keywords: convection diffusion; space; time; diffusion equations ... See more keywords
A Sparse Grid Stochastic Collocation Upwind Finite Volume Element Method for the Constrained Optimal Control Problem Governed by Random Convection Diffusion Equations
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DOI: 10.1007/s10915-018-0713-y
Abstract: In this paper, we deal with an optimal control problem governed by the convection diffusion equations with random field in its coefficients. Mathematically, we prove the necessary and sufficient optimality conditions for the optimal control… read more here.
Keywords: convection diffusion; control; control problem; problem governed ... See more keywords
Error Estimates for First- and Second-Order Lagrange–Galerkin Moving Mesh Schemes for the One-Dimensional Convection–Diffusion Equation
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DOI: 10.1007/s10915-024-02673-4
Abstract: A new moving mesh scheme based on the Lagrange–Galerkin method for the approximation of the one-dimensional convection–diffusion equation is studied. The mesh movement is prescribed by a discretized dynamical system for the nodal points. This… read more here.
Keywords: diffusion equation; lagrange galerkin; moving mesh; error estimates ... See more keywords
Edge-Averaged Virtual Element Methods for Convection-Diffusion and Convection-Dominated Problems
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DOI: 10.1007/s10915-025-02984-0
Abstract: This paper develops edge-averaged virtual element (EAVE) methodologies to address convection-diffusion problems effectively in the convection-dominated regime. It introduces a variant of EAVE that ensures monotonicity (producing an M-matrix) on Voronoi polygonal meshes, provided their… read more here.
Keywords: averaged virtual; edge averaged; convection; convection diffusion ... See more keywords
Supercloseness of the HDG Method on Shishkin Mesh for a Singularly Perturbed Convection Diffusion Problem in 2D
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DOI: 10.1007/s10915-025-03056-z
Abstract: This paper presents the first analysis of parameter-uniform convergence for a hybridizable discontinuous Galerkin (HDG) method applied to a singularly perturbed convection-diffusion problem in 2D using a Shishkin mesh. The primary difficulty lies in accurately… read more here.
Keywords: singularly perturbed; method; convection diffusion; convection ... See more keywords
Layer resolving fitted mesh method for parabolic convection-diffusion problems with a variable diffusion
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DOI: 10.1007/s12190-021-01562-5
Abstract: In this paper, we constructed a fitted mesh finite difference method for solving a class of time-dependent singularly perturbed turning point convection-diffusion problems whose solution exhibits an interior layer. The diffusion coefficient in the underlying… read more here.
Keywords: diffusion problems; convection diffusion; method; diffusion ... See more keywords