TY - GEN
T1 - A simple preconditioner for the SIPG discretization of linear elasticity equations
AU - Ayuso, B.
AU - Georgiev, I.
AU - Kraus, J.
AU - Zikatanov, L.
N1 - Copyright:
Copyright 2011 Elsevier B.V., All rights reserved.
PY - 2011
Y1 - 2011
N2 - We deal with the solution of the systems of linear algebraic equations arising from Symmetric Interior Penalty discontinuous Galerkin (SIPG) discretization of linear elasticity problems in primal (displacement) formulation. The main focus of the paper is on constructing a uniform preconditioner which is based on a natural splitting of the space of piecewise linear discontinuous functions. The presented approach has recently been introduced in [2] in the context of designing subspace correction methods for scalar elliptic partial differential equations and is extended here to linear elasticity equations, i.e., a class of vector field problems. Similar to the scalar case the solution of the linear algebraic system corresponding to the SIPG method is reduced to the solution of a problem arising from discretization by nonconforming Crouzeix-Raviart elements plus the solution of a well-conditioned problem on the complementary space.
AB - We deal with the solution of the systems of linear algebraic equations arising from Symmetric Interior Penalty discontinuous Galerkin (SIPG) discretization of linear elasticity problems in primal (displacement) formulation. The main focus of the paper is on constructing a uniform preconditioner which is based on a natural splitting of the space of piecewise linear discontinuous functions. The presented approach has recently been introduced in [2] in the context of designing subspace correction methods for scalar elliptic partial differential equations and is extended here to linear elasticity equations, i.e., a class of vector field problems. Similar to the scalar case the solution of the linear algebraic system corresponding to the SIPG method is reduced to the solution of a problem arising from discretization by nonconforming Crouzeix-Raviart elements plus the solution of a well-conditioned problem on the complementary space.
UR - http://www.scopus.com/inward/record.url?scp=79951964975&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=79951964975&partnerID=8YFLogxK
U2 - 10.1007/978-3-642-18466-6_42
DO - 10.1007/978-3-642-18466-6_42
M3 - Conference contribution
AN - SCOPUS:79951964975
SN - 9783642184659
T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
SP - 353
EP - 361
BT - Numerical Methods and Applications - 7th International Conference, NMA 2010, Revised Papers
T2 - 7th International Conference on Numerical Methods and Applications, NMA 2010
Y2 - 20 August 2010 through 24 August 2010
ER -