Journal
BIT NUMERICAL MATHEMATICS
Volume 60, Issue 1, Pages 235-260Publisher
SPRINGER
DOI: 10.1007/s10543-019-00773-4
Keywords
Boundary value correction; Lagrange multiplier; Dirichlet boundary conditions
Funding
- EPSRC, UK [EP/P01576X/1]
- Swedish Foundation [AM13-0029]
- Swedish Research Council [2013-4708, 2017-03911, 2018-05262]
- Swedish strategic research programme eSSENCE
- Swedish Research Council [2018-05262] Funding Source: Swedish Research Council
- EPSRC [EP/P01576X/1] Funding Source: UKRI
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We propose a boundary value correction approach for cases when curved boundaries are approximated by straight lines (planes) and Lagrange multipliers are used to enforce Dirichlet boundary conditions. The approach allows for optimal order convergence for polynomial order up to 3. We show the relation to a Taylor series expansion approach previously used in the context of Nitsche's method and, in the case of inf-sup stable multiplier methods, prove a priori error estimates with explicit dependence on the meshsize and distance between the exact and approximate boundary.
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