A Godunov-mixed finite element method on changing meshes for the nonlinear Sobolev equations
type: Item
instance of: scholarly article
title: A Godunov-mixed finite element method on changing meshes for the nonlinear Sobolev equations
zbMATH Open document ID: 1259.65152
DOI: 10.1155/2012/413718
published in: Abstract and Applied Analysis
publication date: 2013-02-04T00:00:00Z
review text: Summary: A Godunov-mixed finite element method on changing meshes is presented to simulate the nonlinear Sobolev equations. The convection term of the nonlinear Sobolev equations is approximated by a Godunov-type procedure and the diffusion term by an expanded mixed finite element method. The method can simultaneously approximate the scalar unknown and the vector flux effectively, reducing the continuity of the finite element space. Almost optimal error estimates in \(L^2\)-norm under very general changes in the mesh can be obtained. Finally, a numerical experiment is given to illustrate the efficiency of the method.
Mathematics Subject Classification ID: 65M60
Mathematics Subject Classification ID: 35Q35
Mathematics Subject Classification ID: 65M06
Mathematics Subject Classification ID: 65M15
zbMATH DE Number: 6134083
zbMATH Keywords: Godunov-mixed finite element method
zbMATH Keywords: nonlinear Sobolev equations
zbMATH Keywords: error estimates
zbMATH Keywords: numerical experiment
Wikidata QID: Q58696561
author: Tongjun Sun
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1155/2012/413718
OpenAlex ID: W2112192347
cites work: Moving Finite Elements. I
cites work: Moving Finite Elements. II
cites work: Q4894372
cites work: Q3804124
cites work: An upwind-mixed method on changing meshes for two-phase miscible flow in porous media
cites work: Basic concepts in the theory of seepage of homogeneous liquids in fissured rocks [strata]
cites work: Q3478883
cites work: A cooling process according to two-temperature theory of heat conduction
cites work: Time-Stepping Galerkin Methods for Nonlinear Sobolev Partial Differential Equations
cites work: Q3476240
cites work: Finite difference-streamline diffusion method for quasi-linear Sobolev equations
cites work: Error estimates for a discontinuous Galerkin method with interior penalties applied to nonlinear Sobolev equations
cites work: Two new least-squares mixed finite element procedures for convection-dominated Sobolev equations
cites work: An unsplit, higher order Godunov method for scalar conservation laws in multiple dimensions
cites work: Godunov-mixed methods for immiscible displacement
cites work: A second-order projection method for the incompressible Navier-Stokes equations
cites work: Godunov-Mixed Methods for Advective Flow Problems in One Space Dimension
cites work: Godunov-Mixed Methods for Advection-Diffusion Equations in Multidimensions
cites work: Mixed Finite Elements for Elliptic Problems with Tensor Coefficients as Cell-Centered Finite Differences
cites work: Q4136469
cites work: Global Estimates for Mixed Methods for Second Order Elliptic Equations
description: scientific article; zbMATH DE number 6134083