Superconvergence of the local discontinuous Galerkin method for linear fourth-order time-dependent problems in one space dimension

DOI10.1093/imanum/drr047zbMath1258.65083OpenAlexW2112241502MaRDI QIDQ4649625

Chi-Wang Shu, Xiong Meng, Boying Wu

Publication date: 12 November 2012

Published in: IMA Journal of Numerical Analysis (Search for Journal in Brave)

Full work available at URL: https://semanticscholar.org/paper/184d306d7728c720858948c13340fb4817c8d26d

zbMATH Keywords

error estimatesnumerical experimentsKuramoto-Sivashinsky equationsuperconvergenceinitial boundary value problemlocal discontinuous Galerkin methodfourth-order problems

Mathematics Subject Classification ID

PDEs in connection with fluid mechanics (35Q35) Initial-boundary value problems for higher-order parabolic equations (35K35) 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)

Related Items

A mixed discontinuous Galerkin method without interior penalty for time-dependent fourth order problems, Some recent developments in superconvergence of discontinuous Galerkin methods for time-dependent partial differential equations, Error analysis of the semi-discrete local discontinuous Galerkin method for compressible miscible displacement problem in porous media, Isogeometric analysis and error estimates for high order partial differential equations in fluid dynamics, Asymptotically exact a posteriori local discontinuous Galerkin error estimates for the one-dimensional second-order wave equation, Optimal energy conserving local discontinuous Galerkin methods for second-order wave equation in heterogeneous media, Superconvergence of the local discontinuous Galerkin method for nonlinear convection-diffusion problems, Superconvergence of local discontinuous Galerkin methods for partial differential equations with higher order derivatives, The local discontinuous Galerkin finite element methods for Caputo-type partial differential equations: numerical analysis, Stability analysis and error estimates of implicit Runge-Kutta local discontinuous Galerkin methods for linear bi-harmonic equation, A new three-field formulation of the biharmonic problem and its finite element discretization, Fully discrete local discontinuous Galerkin methods for some time-fractional fourth-order problems, Local discontinuous Galerkin method for a nonlinear time-fractional fourth-order partial differential equation, A Posteriori Error Estimates for a Local Discontinuous Galerkin Approximation of Semilinear Second-Order Elliptic Problems on Cartesian Grids, \(hp\)-FEM for a stabilized three-field formulation of the biharmonic problem, The local discontinuous Galerkin method for the fourth-order Euler-Bernoulli partial differential equation in one space dimension. I: Superconvergence error analysis, The optimal error estimate and superconvergence of the local discontinuous Galerkin methods for one-dimensional linear fifth order time dependent equations, Superconvergence of the local discontinuous Galerkin method for the linearized Korteweg-de Vries equation, Optimal error estimates for discontinuous Galerkin methods based on upwind-biased fluxes for linear hyperbolic equations, Superconvergence of the local discontinuous Galerkin method for the sine-Gordon equation on Cartesian grids, Superconvergence of local discontinuous Galerkin methods with generalized alternating fluxes for 1D linear convection-diffusion equations, Local discontinuous Galerkin methods for diffusive-viscous wave equations