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Mortar element methods for parabolic problems
Author(s) -
Patel Ajit,
Pani Amiya K.,
Nataraj Neela
Publication year - 2008
Publication title -
numerical methods for partial differential equations
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.901
H-Index - 61
eISSN - 1098-2426
pISSN - 0749-159X
DOI - 10.1002/num.20327
Subject(s) - mathematics , mortar methods , lagrange multiplier , finite element method , mortar , discretization , projection (relational algebra) , backward euler method , partial differential equation , scheme (mathematics) , mathematical analysis , boundary value problem , mixed finite element method , mathematical optimization , algorithm , structural engineering , archaeology , engineering , history
In this article a standard mortar finite element method and a mortar element method with Lagrange multiplier are used for spatial discretization of a class of parabolic initial‐boundary value problems. Optimal error estimates in L ∞ ( L 2 ) and L ∞ ( H 1 )‐norms for semidiscrete methods for both the cases are established. The key feature that we have adopted here is to introduce a modified elliptic projection. In the standard mortar element method, a completely discrete scheme using backward Euler scheme is discussed and optimal error estimates are derived. The results of numerical experiments support the theoretical results obtained in this article. © 2008 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 2008