UNIFIED ERROR ANALYSIS OF DISCONTINUOUS GALERKIN METHODS FOR PARABOLIC OBSTACLE PROBLEM

被引:0
作者
Majumder, Papri [1 ]
机构
[1] Indian Inst Technol Delhi, Dept Math, New Delhi 110016, India
关键词
finite element; discontinuous Galerkin method; parabolic obstacle problem; FINITE-ELEMENT-METHOD; APPROXIMATION; SPACE; CONVECTION; FEM;
D O I
10.21136/AM.2021.0030-20
中图分类号
O29 [应用数学];
学科分类号
070104 ;
摘要
We introduce and study various discontinuous Galerkin (DG) finite element approximations for a parabolic variational inequality associated with a general obstacle problem in Double-struck capital R-d (d = 2, 3). For the fully-discrete DG scheme, we employ a piecewise linear finite element space for spatial discretization, whereas the time discretization is carried out with the implicit backward Euler method. We present a unified error analysis for all well known symmetric and non-symmetric DG fully discrete schemes, and derive error estimate of optimal order O(h + Delta t) in an energy norm. Moreover, the analysis is performed without any assumptions on the speed of propagation of the free boundary and only the realistic regularity u(t) is an element of L-2(0, T; L-2(Omega)) is assumed. Further, we present some numerical experiments to illustrate the performance of the proposed methods.
引用
收藏
页码:673 / 699
页数:27
相关论文
共 47 条
[1]   Unified analysis of discontinuous Galerkin methods for elliptic problems [J].
Arnold, DN ;
Brezzi, F ;
Cockburn, B ;
Marini, LD .
SIAM JOURNAL ON NUMERICAL ANALYSIS, 2002, 39 (05) :1749-1779
[2]   AN INTERIOR PENALTY FINITE-ELEMENT METHOD WITH DISCONTINUOUS ELEMENTS [J].
ARNOLD, DN .
SIAM JOURNAL ON NUMERICAL ANALYSIS, 1982, 19 (04) :742-760
[3]   NONCONFORMING ELEMENTS IN FINITE-ELEMENT METHOD WITH PENALTY [J].
BABUSKA, I ;
ZLAMAL, M .
SIAM JOURNAL ON NUMERICAL ANALYSIS, 1973, 10 (05) :863-875
[4]   hp-adaptive IPDG/TDG-FEM for parabolic obstacle problems [J].
Banz, Lothar ;
Stephan, Ernst P. .
COMPUTERS & MATHEMATICS WITH APPLICATIONS, 2014, 67 (04) :712-731
[5]  
Bassi F., 1997, 2 EUROPEAN C TURBOMA, P99
[6]  
BERGER AE, 1977, MATH COMPUT, V31, P619, DOI 10.1090/S0025-5718-1977-0438707-8
[7]  
Brenner SC, 2008, ELECTRON T NUMER ANA, V30, P107
[8]  
BREZIS H, 1972, J MATH PURE APPL, V51, P1
[9]  
Brezis H., 1973, OPERATEURS MAXIMAUX, V5
[10]  
Brezzi F, 2000, NUMER METH PART D E, V16, P365, DOI 10.1002/1098-2426(200007)16:4<365::AID-NUM2>3.0.CO