A novel two-step streamline-diffusion FEM for singularly perturbed 2D parabolic PDEs

DOI10.1016/j.apnum.2021.10.010zbMath1484.65208OpenAlexW3205638700WikidataQ114208186 ScholiaQ114208186MaRDI QIDQ2058401

Yanyan Li

Publication date: 9 December 2021

Published in: Applied Numerical Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.apnum.2021.10.010

zbMATH Keywords

stabilityerror analysisShishkin meshoperator-splitting methodADI methodSDFEMsingularly perturbed 2D parabolic PDEs

Mathematics Subject Classification ID

Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs (65M12) Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs (65M60) Error bounds for initial value and initial-boundary value problems involving PDEs (65M15)

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Cites Work

• Unnamed Item
• Crank-Nicolson ADI Galerkin finite element method for two-dimensional fractional Fitzhugh-Nagumo monodomain model
• Operator-splitting finite element algorithms for computations of high-dimensional parabolic problems
• Finite element methods for time-dependent convection-diffusion-reaction equations with small diffusion
• Finite element methods of an operator splitting applied to population balance equations
• Layer-adapted meshes for reaction-convection-diffusion problems
• A new finite element formulation for computational fluid dynamics. VI. Convergence analysis of the generalized SUPG formulation for linear time- dependent multidimensional advective-diffusive systems
• A fractional step method on a special mesh for the resolution of multidimensional evolutionary convection-diffusion problems
• A new ADI technique for two-dimensional parabolic equation with an integral condition
• Approximation of continuous surface differential operators with the generalized moving least-squares (GMLS) method for solving reaction-diffusion equation
• Higher-order convergence with fractional-step method for singularly perturbed 2D parabolic convection-diffusion problems on Shishkin mesh
• Alternating direction numerical scheme for singularly perturbed 2D degenerate parabolic convection-diffusion problems
• Convergence analysis of weak Galerkin flux-based mixed finite element method for solving singularly perturbed convection-diffusion-reaction problem
• An operator-splitting Galerkin/SUPG finite element method for population balance equations : stability and convergence
• Error Analysis of the SUPG Finite Element Discretization of Evolutionary Convection-Diffusion-Reaction Equations
• Robust Numerical Methods for Singularly Perturbed Differential Equations
• Time‐splitting procedures for the solution of the two‐dimensional transport equation
• A heterogeneous alternating-direction method for a micro-macro dilute polymeric fluid model
• Analysis of Some Difference Approximations for a Singular Perturbation Problem Without Turning Points
• The Mathematical Theory of Finite Element Methods
• The necessity of Shishkin decompositions