A new space-time continuous Galerkin method with mesh modification for Sobolev equations

DOI10.1016/j.jmaa.2016.03.035zbMath1382.65335OpenAlexW2298568405MaRDI QIDQ269416

Zhihui Zhao, Hong Li, Zhen-Dong Luo

Publication date: 18 April 2016

Published in: Journal of Mathematical Analysis and Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jmaa.2016.03.035

zbMATH Keywords

numerical examplescontinuous Galerkin methodoptimal rates of convergenceSobolev equations

Mathematics Subject Classification ID

Initial-boundary value problems for higher-order parabolic equations (35K35) Singular perturbations in context of PDEs (35B25) Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs (65M12) Theoretical approximation in context of PDEs (35A35) Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs (65M60)

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The reduced-dimension technique for the unknown solution coefficient vectors in the Crank-Nicolson finite element method for the Sobolev equation ⋮ The reduced-order method of continuous space-time finite element scheme for the non-stationary incompressible flows ⋮ An optimized finite difference Crank-Nicolson iterative scheme for the 2D Sobolev equation ⋮ Proper orthogonal decomposition reduced-order extrapolation continuous space-time finite element method for the two-dimensional unsteady Stokes equation ⋮ Convergence of a space-time continuous Galerkin method for the wave equation ⋮ Analysis of a space-time continuous Galerkin method for convection-dominated Sobolev equations ⋮ A reduced‐order extrapolating space–time continuous finite element method for the 2D Sobolev equation ⋮ Unnamed Item ⋮ Application of spectral element method for solving Sobolev equations with error estimation ⋮ A localisation technique based on radial basis function partition of unity for solving Sobolev equation arising in fluid dynamics ⋮ A RBF partition of unity collocation method based on finite difference for initial-boundary value problems ⋮ A reduced-order extrapolated finite difference iterative scheme based on POD method for 2D Sobolev equation ⋮ Maximum error estimates of two linearized compact difference schemes for two-dimensional nonlinear Sobolev equations ⋮ Localized meshless approaches based on theta method and BDF2 for nonlinear Sobolev equation arising from fluid dynamics

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