On the order of pointwise convergence of some boundary element methods. Part I. Operators of negative and zero order

R. Rannacher; W. L. Wendland

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique (1985)

  • Volume: 19, Issue: 1, page 65-87
  • ISSN: 0764-583X

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Rannacher, R., and Wendland, W. L.. "On the order of pointwise convergence of some boundary element methods. Part I. Operators of negative and zero order." ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique 19.1 (1985): 65-87. <http://eudml.org/doc/193442>.

@article{Rannacher1985,
author = {Rannacher, R., Wendland, W. L.},
journal = {ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique},
keywords = {boundary integral equations; strongly elliptic pseudodifferential equations; finite element Galerkin method; convergence; discrete Green functions; Garding's inequality},
language = {eng},
number = {1},
pages = {65-87},
publisher = {Dunod},
title = {On the order of pointwise convergence of some boundary element methods. Part I. Operators of negative and zero order},
url = {http://eudml.org/doc/193442},
volume = {19},
year = {1985},
}

TY - JOUR
AU - Rannacher, R.
AU - Wendland, W. L.
TI - On the order of pointwise convergence of some boundary element methods. Part I. Operators of negative and zero order
JO - ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique
PY - 1985
PB - Dunod
VL - 19
IS - 1
SP - 65
EP - 87
LA - eng
KW - boundary integral equations; strongly elliptic pseudodifferential equations; finite element Galerkin method; convergence; discrete Green functions; Garding's inequality
UR - http://eudml.org/doc/193442
ER -

References

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  1. [1] M S AGRANOVICH, Spectral properties of diffraction problems In The General Method of Natural Vibrations in Diffraction Theory (Russian) (N N Voitovic, K Z Katzenellenbaum and A N Sivov) Izdat Nauka Moscow 1977 MR484012
  2. [2] D ARNOLD and W L WENDLANDOn the asymptotic convergence of collocation methods Math Comp in print (1983) Zbl0541.65075MR717691
  3. [3] J P AUBIN, Approximation of Elliptic Boundary-Value Problems Wiley-Interscience New York 1972 Zbl0248.65063MR478662
  4. [4] I BABUSKA and A K Aziz, The Mathematical Foundations of the Finite Element Method with Applications to Partial Differential Equations (A K Aziz ed ) pp 3-359, Academic Press, New York 1972 Zbl0259.00014MR347104
  5. [5] T DUPONT and R SCOTT, Constructive polynomial approximation In « Recent Advances in Numerical Analysis » (C de Boor ed ), Proc at MRC Madison Wisconsin, May 1978 Zbl0456.65003
  6. [6] G I ESKIN, Boundary Value Problems for Elliptic Pseudodifferential Equations Trans Math Mon Amer Math Soc Providence, Rhode Island 1981 1981 Zbl0458.35002MR623608
  7. [7] J FREHSE and R RANNACHEREine L 1 -Fehlerabschatzung fur diskrete Grundlosungen in der Methode der finiten ElementeIn « Finite Elemente » Tagungsband Bonn Math Schr 89, 92-114 (1976) Zbl0359.65093MR471370
  8. [8] L HORMANDER, Pseudo-differential operators and non-elliptic boundary problems Annals Math 83, 129-209 (1966) Zbl0132.07402MR233064
  9. [9] L HORMANDER, Fourier intégral operators I Acta mathematica 127, 79-183 (1971) Zbl0212.46601MR388463
  10. [10] G C HSIAO, P KOPP and W L WENDLAND, A Galerkin collocation method for some integral equations of the first kind Computing 25, 89-130 (1980) Zbl0419.65088MR620387
  11. [11] G C HSIAO and W L WENDLAND, Afinite element method for some integral equations of the first kind J Math Anal Appl 58, 449-481 (1977) Zbl0352.45016MR461963
  12. [12] G C HSIAO and W L WENDLANDThe Aubin-Nitsche lemma for integral equations Journal of Integral Equations 3, 299-315 (1981) Zbl0478.45004MR634453
  13. [13] G C HSIAO and W L WENDLANDSuper-approximation for boundary integral methods In Advances in Computer Methods for Partial Differential Equations IV (ed R Vichnevetsky, R S Stepleman), pp 200-206, IMACS, Dept Comp Sc Rutgers Univ New Brunswick 1981 
  14. [14] E MARTENSENPotentialtheorie B G Teubner Stuttgart1968 Zbl0174.42602MR247116
  15. [15] S G MICHLIN, Vorlesungen uber lineare Integralgleichungen Verl der Wiss Berlin1962 MR141959
  16. [16] F NATTERER, Uber die punktweise Konvergenz finiter Elemente Numer Math 25 67-77 (1975) Zbl0331.65073MR474884
  17. [17] J C NEDELEC, Approximation des équations integrales en mecanique et en physique Lecture Notes, Centre de Math Appl Ecole Polytechnique, 91128 Palaiseau, France, 1977 
  18. [18] J C NEDELEC and J PLANCHARD, Une methode variationnelle d'elements finis pour la resolution numérique d un probleme exterieur des R3 Revue Franc Automatique, Inf Rech Oper R 3, 105-129 (1973) Zbl0277.65074MR424022
  19. [19] J A NITSCHE , L -convergence of finite element approximation Second Conference on Finite Elements, Rennes, France, 1975 Zbl0362.65088MR568857
  20. [20] P M PRENTER, Splines and Variational Methods John Wiley & Sons, New York 1975 Zbl0344.65044MR483270
  21. [21] R RANNACHER, Punktweise Konvergenz der Methode der finiten Elemente beim Plattenproblem Manuscripta math 19, 401-416(1976) Zbl0383.65061MR423841
  22. [22] J SARANEN and W L WENDLAND, One the asymptotic convergence of collocation methods with spline functions of even degree, to appear in Math Comp 1985 Zbl0623.65145MR790646
  23. [23] A H SCHATZ and L B WAHLBIN, Maximum norm error estimates in the finite element method for Poisson equation on plane domains with corners Math Comp 32, 73-109 (1978) Zbl0382.65058MR502065
  24. [24] R SCOTTOptimal L -estimates for the finite element method on irregular meshes Math Comp 30, 681-697 (1976) Zbl0349.65060MR436617
  25. [25] E STEPHAN, Solution procedures for interface problems in acoustics and electro-magnetics In Theoretical Acoustics and Numerical Techniques (ed P Filippi), CISM Courses 277, Springer-Verlag, Wien, New York, 291-348 (1983) Zbl0578.76078MR762832
  26. [26] E STEPHAN and W L WENDLAND, Remarks to Galerkin and least squares methods with finite elements for general elliptic problem Manuscripta Geodaetica 1, 93-123 (1976) and Springer Lecture Notes m Math 564, 461-471 (1976) Zbl0353.65067MR520343
  27. [27] G STRANG, Approximation in the finite element method Num Math 19, (1972) Zbl0221.65174MR305547
  28. [28] M TAYLOR, Pseudodifferential Operators Princeton Univ Press, Princeton N J 1981 Zbl0453.47026MR618463
  29. [29] F TRÊVES, Pseudodifferential Operators Plenum Press New York, London 1980 MR597144
  30. [30] W L WENDLAND, On applications and the convergence of boundary integral methods In Treatment of Integral Equations by Numerical Methods (ed T H Baker G F Miller), pp 463-476, Academic Press, London 1982 Zbl0561.65085MR755378
  31. [31] W L WENDLANDBoundary element methods and their asymptotic convergence In Theoretical Acoustics and Numerical Techniques (ed P Filippi), CISM Courses 277 Springer-Verlag, Wien, New York, 135 216 (1983) Zbl0618.65109MR762829

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