A fully discrete \(H^1\)-Galerkin method with quadrature for nonlinear advection-diffusion-reaction equations

DOI10.1007/s11075-007-9066-6zbMath1128.65080OpenAlexW1990295685MaRDI QIDQ877271

N. E. Zubov

Publication date: 19 April 2007

Published in: Numerical Algorithms (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s11075-007-9066-6

zbMATH Keywords

convergenceGalerkin methodleast-squares methodheat equationnumerical experimentsparabolic equationsquadratureadvection-diffusion-reaction equationsnonlinear parabolic advection-diffusion-reaction equations

Mathematics Subject Classification ID

Reaction-diffusion equations (35K57) 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 (8)

\(H^1\) space-time discontinuous finite element method for convection-diffusion equations ⋮ Discrete-time ZD, GD and NI for solving nonlinear time-varying equations ⋮ A Spectrally Accurate Algorithm and Analysis for a Ginzburg--Landau Model on Superconducting Surfaces ⋮ Schrödinger eigenbasis on a class of superconducting surfaces: ansatz, analysis, FEM approximations and computations ⋮ A pseudospectral quadrature method for Navier-Stokes equations on rotating spheres ⋮ Boundary integral formulation and semi-implicit scheme coupling for modeling cells under electrical stimulation ⋮ Continuous and discrete time Zhang dynamics for time-varying 4th root finding ⋮ Multiple traces formulation and semi-implicit scheme for modelling biological cells under electrical stimulation

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Collocation methods for parabolic equations in a single space variable. Based on C\(^1\)-piecewise-polynomial spaces
• Linear and quasilinear elliptic equations
• A $C^1 $ Finite Element Collocation Method for Elliptic Equations
• On the boundary value problem of the biharmonic operator on domains with angular corners
• Simplified Proofs of Error Estimates for the Least Squares Method for Dirichlet's Problem
• Elliptic Partial Differential Equations of Second Order
• Local $H^{-1}$ Galerkin and adjoint local $H^{-1}$ Galerkin procedures for elliptic equations
• A Petrov-Galerkin method with quadrature for elliptic boundary value problems
• A quadrature finite element Galerkin scheme for a biharmonic problem on a rectangular polygon
• Analysis of incompressible miscible displacement in porous media by characteristics collocation method
• Multilevel preconditioners for a quadrature Galerkin solution of a biharmonic problem
• Variational, Geometric, and Level Set Methods in Computer Vision
• Rayleigh‐Ritz‐Galerkin methods for dirichlet's problem using subspaces without boundary conditions
• Least Squares Methods for 2mth Order Elliptic Boundary-Value Problems
• Superapproximation and commutator properties of discrete orthogonal projections for continuous splines
• Orthogonal spline collocation methods for partial differential equations

This page was built for publication: A fully discrete \(H^1\)-Galerkin method with quadrature for nonlinear advection-diffusion-reaction equations