Paper Info
Title
Conforming and discontinuous Galerkin FEM in space for solving parabolic obstacle problem
Abstract
In this article, we propose and analyze conforming and discontinuous Galerkin (DG) finite element methods for numerical approximation of the solution of the parabolic variational inequality associated with a general obstacle in Rd(d=2,3). For fully discrete conforming method, we use globally continuous and piecewise linear finite element space. Whereas for the fully-discrete DG scheme, we employ piecewise linear finite element space for spatial discretization. The time discretization has been done by using the implicit backward Euler method. We present the error analysis for the conforming and the DG fully discrete schemes and derive an error estimate of optimal order O(h+Δt) in a certain energy norm defined precisely in the article. The analysis is performed without any assumptions on the speed of propagation of the free boundary but only assumes the pragmatic regularity that ut∈L2(0,T;L2(Ω)). The obstacle constraints are incorporated at the Lagrange nodes of the triangular mesh and the analysis exploits the Lagrange interpolation. We present some numerical experiment to illustrate the performance of the proposed methods.
Year
DOI
Venue
2019
10.1016/j.camwa.2019.06.022
Computers & Mathematics with Applications
Keywords
Field
DocType
Finite element,Discontinuous Galerkin method,Parabolic obstacle problem
Discontinuous Galerkin method,Lagrange polynomial,Discretization,Mathematical analysis,Finite element method,Obstacle problem,Piecewise linear function,Backward Euler method,Mathematics,Variational inequality
Journal
Volume
Issue
ISSN
78
12
0898-1221
Citations 
PageRank 
References 
0
0.34
0
Authors
2
Name
Order
Citations
PageRank
Thirupathi Gudi113514.43
Papri Majumder201.01