Legendre spectral element method (LSEM) to simulate the two-dimensional system of nonlinear stochastic advection–reaction–diffusion models

DOI10.1080/00036811.2020.1807007zbMath1487.65160arXiv1904.06263OpenAlexW3080754551MaRDI QIDQ5072943

Mostafa Abbaszadeh, Thomas Wick, Amirreza Khodadadian, Mehdi Dehghan

Publication date: 5 May 2022

Published in: Applicable Analysis (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1904.06263

zbMATH Keywords

error estimatestochastic PDEsspectral element method (SEM)nonlinear system of advection-reaction-diffusion equation

Mathematics Subject Classification ID

Spectral, collocation and related methods for boundary value problems involving PDEs (65N35) Hydrology, hydrography, oceanography (86A05) 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) PDEs with randomness, stochastic partial differential equations (35R60)

Related Items (4)

Analysis of the linearly energy- and mass-preserving finite difference methods for the coupled Schrödinger-Boussinesq equations ⋮ A three level linearized compact difference scheme for a fourth-order reaction-diffusion equation ⋮ A two-grid spectral method to study of dynamics of dense discrete systems governed by Rosenau-Burgers' equation ⋮ Stochastic suicide substrate reaction model

Cites Work

• Unnamed Item
• A spectral element method for solving the Pennes bioheat transfer equation by using triangular and quadrilateral elements
• Krylov implicit integration factor WENO methods for semilinear and fully nonlinear advection-diffusion-reaction equations
• A Legendre spectral element method on a large spatial domain to solve the predator-prey system modeling interacting populations
• A local radial basis function method for advection-diffusion-reaction equations on complexly shaped domains
• The spectral methods for parabolic Volterra integro-differential equations
• A spectral element method to price European options. I. Single asset with and without jump diffusion
• A spectral element approximation to price European options with one asset and stochastic volatility
• Weak convergence analysis of the linear implicit Euler method for semilinear stochastic partial differential equations with additive noise
• An error analysis of a finite element method for a system of nonlinear advection-diffusion-reaction equations
• Stochastic partial differential equations in groundwater hydrology. I: Theory
• Strong and weak Lagrange-Galerkin spectral element methods for the shallow water equations
• Local radial basis function collocation method for solving thermo-driven fluid-flow problems with free surface
• A combination of proper orthogonal decomposition-discrete empirical interpolation method (POD-DEIM) and meshless local RBF-DQ approach for prevention of groundwater contamination
• An `empirical interpolation' method: Application to efficient reduced-basis discretization of partial differential equations
• Coupled nonlinear advection-diffusion-reaction system for prevention of groundwater contamination by modified upwind finite volume element method
• Lattice Boltzmann method for groundwater flow in non-orthogonal structured lattices
• Remediation of contaminated groundwater by meshless local weak forms
• Alternating direction implicit-spectral element method (ADI-SEM) for solving multi-dimensional generalized modified anomalous sub-diffusion equation
• Analysis and application of the interpolating element free Galerkin (IEFG) method to simulate the prevention of groundwater contamination with application in fluid flow
• Crank-Nicolson/Galerkin spectral method for solving two-dimensional time-space distributed-order weakly singular integro-partial differential equation
• Multi-index stochastic collocation for random PDEs
• Space-time spectral method for a weakly singular parabolic partial integro-differential equation on irregular domains
• Numerical models for 2D free boundary analysis of groundwater in slopes stabilized by drain trenches
• Efficient Spectral-Galerkin Method I. Direct Solvers of Second- and Fourth-Order Equations Using Legendre Polynomials
• A spectral element method using the modal basis and its application in solving second‐order nonlinear partial differential equations

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