[inline-graphic not available: see fulltext]-Error Estimates of the Extrapolated Crank-Nicolson Discontinuous Galerkin Approximations for Nonlinear Sobolev Equations

被引：0
作者：
MiRay Ohm
HyunYoung Lee
JunYong Shin
机构：
[1] Dongseo University,Division of Information Systems Engineering
[2] Kyungsung University,Department of Mathematics
[3] Pukyong National University,Division of Mathematical Sciences
来源：
Journal of Inequalities and Applications | / 2010卷
关键词：
Galerkin Method; Constant Independent; Spatial Discretization; Discrete Method; Discrete Version;
D O I：
暂无
中图分类号：
学科分类号：
摘要：
We analyze discontinuous Galerkin methods with penalty terms, namely, symmetric interior penalty Galerkin methods, to solve nonlinear Sobolev 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 [inline-graphic not available: see fulltext] error estimates of discontinuous Galerkin approximations in both spatial direction and temporal direction.
引用
收藏
相关论文
共 30 条
  • [1] Barenblatt GI(1960)Basic concepts in the theory of seepage of homogeneous liquids in fissured rocks Journal of Applied Mathematics and Mechanics 24 1286-1303
  • [2] Zheltov IP(1968)On a theory of heat conduction involving two temperatures Zeitschrift für Angewandte Mathematik und Physik 19 614-627
  • [3] Kochina IN(1972)A quasilinear parabolic and a related third order problem Journal of Mathematical Analysis and Applications 40 327-335
  • [4] Chen PJ(1978)Time-stepping Galerkin methods for nonlinear Sobolev partial differential equations SIAM Journal on Numerical Analysis 15 1125-1150
  • [5] Gurtin ME(1974)A cooling process according to two-temperature theory of heat conduction Journal of Mathematical Analysis and Applications 45 23-31
  • [6] Davis PL(1981)Superconvergence of a finite element approximation to the solution of a Sobolev equation in a single space variable Mathematics of Computation 36 53-63
  • [7] Ewing RE(1982)An interior penalty finite element method with discontinuous elements SIAM Journal on Numerical Analysis 19 742-760
  • [8] Ting TW(1985)Error estimates of a Galerkin method for some nonlinear Sobolev equations in one space dimension Numerische Mathematik 47 139-157
  • [9] Arnold DN(1990)Galerkin methods for nonlinear Sobolev equations Aequationes Mathematicae 40 54-66
  • [10] Douglas, J(1992)Finite element methods for nonlinear Sobolev equations with nonlinear boundary conditions Journal of Mathematical Analysis and Applications 165 180-191
123