A finite volume element method for a non-linear elliptic problem Academic Article

abstract

• We consider a finite volume discretization of second-order non-linear elliptic boundary value problems on polygonal domains. Using relatively standard assumptions we show the existence of the finite volume solution. Furthermore, for a sufficiently small data the uniqueness of the finite volume solution may also be deduced. We derive error estimates in H1-, L2- and L-norm for small data and convergence in H1-norm for large data. In addition a Newton's method is analysed for the approximation of the finite volume solution and numerical experiments are presented. Copyright 2005 John Wiley & Sons, Ltd.

authors

• Lazarov, Raytcho

published proceedings

• NUMERICAL LINEAR ALGEBRA WITH APPLICATIONS

author list (cited authors)

• Chatzipantelidis, P., Ginting, V., & Lazarov, R. D.

citation count

• 36

complete list of authors

• Chatzipantelidis, P||Ginting, V||Lazarov, RD

publication date

• January 2005

publisher

• Wiley  Publisher

published in

• Numerical Linear Algebra with Applications  Journal

keywords

• Error Estimates
• Finite Volume Element Method
• Fixed Point Iterations
• Newton's Method
• Non-linear Elliptic Equation

Digital Object Identifier (DOI)

• 10.1002/nla.439

start page

• 515

end page

• 546

volume

• 12

issue

• 5-6

URL

• http%3A%2F%2Fdx.doi.org%2F10.1002%2Fnla.439