East Asian mathematical journal

The Youngnam Mathematical Society (영남수학회)
권호 표지
DOI QR코드

DOI QR Code

A PRIORI $L^2$-ERROR ESTIMATES OF THE CRANK-NICOLSON DISCONTINUOUS GALERKIN APPROXIMATIONS FOR NONLINEAR PARABOLIC EQUATIONS

  • Ahn, Min-Jung (DEPARTMENT OF MATHEMATICS KYUNGSUNG UNIVERSITY) ;
  • Lee, Min-A (DEPARTMENT OF MATHEMATICS DONGSEO UNIVERSITY)
  • Received : 2010.03.16
  • Accepted : 2010.11.01
  • Published : 2010.11.30
Download PDF
⟨ Previous Next ⟩

Abstract

In this paper, we analyze discontinuous Galerkin methods with penalty terms, namly symmetric interior penalty Galerkin methods, to solve nonlinear parabolic equations. We construct finite element spaces on which we develop fully discrete approximations using extrapolated Crank-Nicolson method. We adopt an appropriate elliptic-type projection, which leads to optimal ${\ell}^{\infty}$ ($L^2$) error estimates of discontinuous Galerkin approximations in both spatial direction and temporal direction.

Keywords