Superconvergence of local discontinuous Galerkin methods for partial differential equations with higher order derivatives

DOI10.1007/s10915-017-0377-zzbMath1429.65226OpenAlexW2587087357MaRDI QIDQ1676923

Qiumei Huang, Waixiang Cao

Publication date: 10 November 2017

Published in: Journal of Scientific Computing (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s10915-017-0377-z

zbMATH Keywords

superconvergencelocal discontinuous Galerkin methodRadau pointscell averagehigh order derivative

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)

Related Items (13)

Superconvergence analysis of the Runge-Kutta discontinuous Galerkin method with upwind-biased numerical flux for two-dimensional linear hyperbolic equation ⋮ Some recent developments in superconvergence of discontinuous Galerkin methods for time-dependent partial differential equations ⋮ Continuous/discontinuous Galerkin difference discretizations of high-order differential operators ⋮ Accuracy-enhancement of discontinuous Galerkin methods for PDEs containing high order spatial derivatives ⋮ Fourier analysis of the local discontinuous Galerkin method for the linearized KdV equation ⋮ Superconvergent flux recovery of the Rannacher-Turek nonconforming element ⋮ Superconvergence of the local discontinuous Galerkin method for one dimensional nonlinear convection-diffusion equations ⋮ Superconvergence analysis of the ultra-weak local discontinuous Galerkin method for one dimensional linear fifth order equations ⋮ Superconvergence of the Crouzeix-Raviart element for elliptic equation ⋮ An Oscillation-free Discontinuous Galerkin Method for Scalar Hyperbolic Conservation Laws ⋮ Superconvergence analysis of local discontinuous Galerkin methods for linear convection-diffusion equations in one space dimension ⋮ Analysis of optimal superconvergence of an ultraweak-local discontinuous Galerkin method for a time dependent fourth-order equation ⋮ A class of efficient Hamiltonian conservative spectral methods for Korteweg-de Vries equations

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