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Convergence analysis of an hp finite element method for singularly perturbed transmission problems in smooth domains
Author(s) -
Nicaise Serge,
Xenophontos Christos
Publication year - 2013
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.21793
Subject(s) - mathematics , exponential function , rate of convergence , mathematical analysis , robustness (evolution) , finite element method , domain (mathematical analysis) , singular perturbation , convergence (economics) , boundary value problem , polynomial , boundary (topology) , partial differential equation , computer science , computer network , channel (broadcasting) , biochemistry , chemistry , physics , economics , gene , economic growth , thermodynamics
We consider a two‐dimensional singularly perturbed transmission problem with two different diffusion coefficients, in a domain with smooth (analytic) boundary. The solution will contain boundary layers only in the part of the domain where the diffusion coefficient is high and interface layers along the interface. Utilizing existing and newly derived regularity results for the exact solution, we prove the robustness of an h p finite element method for its approximation. Under the assumption of analytic input data, we show that the method converges at an “exponential” rate, provided the mesh and polynomial degree distribution are chosen appropriately. Numerical results illustrating our theoretical findings are also included. © 2013 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2013