Application of spectral element method for solving Sobolev equations with error estimation

DOI10.1016/j.apnum.2020.08.010zbMath1452.65271OpenAlexW3062230732MaRDI QIDQ2202446

Nasim Shafieeabyaneh, Mehdi Dehghan, Mostafa Abbaszadeh

Publication date: 18 September 2020

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

Full work available at URL: https://doi.org/10.1016/j.apnum.2020.08.010

zbMATH Keywords

energy methoderror estimateSobolev equationsstability and convergence analysisLegendre spectral element methodmigration of the moisture in soilmotion of a fluid in the fissured rock

Mathematics Subject Classification ID

Fluid-solid interactions (including aero- and hydro-elasticity, porosity, etc.) (74F10) Flows in porous media; filtration; seepage (76S05) Finite difference methods applied to problems in fluid mechanics (76M20) Spectral methods applied to problems in fluid mechanics (76M22) Fourier series in special orthogonal functions (Legendre polynomials, Walsh functions, etc.) (42C10) Finite difference methods for initial value and initial-boundary value problems involving PDEs (65M06) Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs (65M12) Spectral, collocation and related methods for initial value and initial-boundary value problems involving PDEs (65M70) Error bounds for initial value and initial-boundary value problems involving PDEs (65M15) Compressible fluids and gas dynamics (76N99)

Related Items

An accurate approach based on the orthonormal shifted discrete Legendre polynomials for variable-order fractional Sobolev equation, Conforming virtual element methods for Sobolev equations, A stabilizer free weak Galerkin finite element method for second‐order Sobolev equation, A linearlized mass-conservative fourth-order block-centered finite difference method for the semilinear Sobolev equation with variable coefficients, Two linearized second-order block-centered finite difference methods for nonlinear Sobolev equations, A hybrid approach established upon the Müntz‐Legender functions and 2D Müntz‐Legender wavelets for fractional Sobolev equation, A localisation technique based on radial basis function partition of unity for solving Sobolev equation arising in fluid dynamics, Finite difference/generalized Hermite spectral method for the distributed-order time-fractional reaction-diffusion equation on multi-dimensional unbounded domains, One-parameter orthogonal spline collocation methods for nonlinear two-dimensional Sobolev equations with time-variable delay, Maximum error estimates of two linearized compact difference schemes for two-dimensional nonlinear Sobolev equations

Uses Software

• Matlab

Cites Work

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