no. 1
L ∞ -convergence of finite element Galerkin approximations for parabolic problems
RAIRO. Analyse numérique, Tome 13 (1979) no. 1, pp. 31-54. 
@article{M2AN_1979__13_1_31_0,
     author = {Nitsche, Joachim A.},
     title = {$L_\infty $-convergence of finite element {Galerkin} approximations for parabolic problems},
     journal = {RAIRO. Analyse num\'erique},
     pages = {31--54},
     publisher = {Centrale des revues, Dunod-Gauthier-Villars},
     address = {Montreuil},
     volume = {13},
     number = {1},
     year = {1979},
     mrnumber = {527037},
     zbl = {0401.65069},
     language = {en},
     url = {http://www.numdam.org/item/M2AN_1979__13_1_31_0/}
}
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Nitsche, Joachim A. $L_\infty $-convergence of finite element Galerkin approximations for parabolic problems. RAIRO. Analyse numérique, Tome 13 (1979) no. 1, pp. 31-54. http://www.numdam.org/item/M2AN_1979__13_1_31_0/

Part a: literature cited

1. D. Archer, An O(h4) cubic spline collocation method for quasilinear parabolic equations, S.I.A.M, J. Numer. Anal., 14, 1977, p. 620-637. | MR | Zbl

2. J. H. Bramble and R. Scott, Simultaneous approximation in scales of Banach spaces (to appear). | MR | Zbl

3. J. H. Bramble, A. Schatz, V. Thomee and L. B. Wahlbin, Some convergence estimates for semidiscrete Galerkin type approximations for parabolic equations, S.I.A.M., J. Numer. Anal, 14, 1977, p. 218-241. | MR | Zbl

4. J. C. Cavendish and C. A. Hall, L∞-convergence of collocation and Galerkin approximations to linear two-point parabolic problems, Aequationes Math , 11, 1974, p. 230-249. | MR | Zbl

5. P. G. Ciarlet and P.-A. Raviart , Interpolation theory over curved elements with applications to finite element methods, Comp. Meth. Appl. Mech. Eng., l, 1972, p. 217-249. | MR | Zbl

6. J. Jr. Douglas and T. Dupont, A finite element collocation method for quasilinear parabolic equations, Math. Comp, 27, 1973, p. 17-18. | MR | Zbl

7. J. Jr. Douglas, T. Dupont and M. Wheeler, Some superconvergence results for an H1-Galerkin procedure for the heat equation, Lecture Notes in Comp. Sci, 10, 1974,p. 491-504. | MR | Zbl

8. F. Natterer, Uber punktweise Konvergenz finiter Elemente, Num. Math., 25, 1975, p. 67-77. | MR | Zbl

9. J. Nitsche, Zur Konvergenz von Naherungsverfahren bezüglich verschiedener Normen, Num. Math., 15, 1970, p. 224-228. | MR | Zbl

10. J. Nitsche, L∞-convergence of finite element approximation. 2nd Conference on Finite Elements, Rennes, 1975. | Zbl

11. J. Nitsche, Über L∞-Abschatzungen von Projektionen auf finite Elemente, Bonner Mathematische Schriften, 89, 1976, p. 13-30. | MR | Zbl

12. J. Nitsche, L∞-convergence of finite element approximations, Lecture Notes in Math., 606, 1977, p. 261-274. | MR | Zbl

13. J. Nitsche and A. Schatz, On local approximation properdes of L2-projection on spline-subspaces, Appl Anal., 2, 1972, p. 161-168. | MR | Zbl

14. R. Scott, Optimal L∞ estimates for the finite element method on irregular meshes, Math. Comp., 30, 1976, p. 681-697. | MR | Zbl

15. V. Thomée, Spline-Galerkin methods for initial-value problems with constant coefficients, Lecture Notes in Math., 363, 1974, p. 164-175. | MR | Zbl

16. L. Wahlbin, On maximum norm error estimates for Galerkin approximation to one-dimensional second order parabolic boundary value problems, S.I.A.M., J. Numer. Anal., 12, 1975, p. 177-182. | MR | Zbl

17. M. B. Wheeler, L∞ estimates of optimal orders for Galerkin methods of one dimensional second order parabolic and hyperbolic equations, S.I.A.M., J. Numer. Anal., 10, 1973, p. 908-913. | MR | Zbl

18. M. Zlamal, Curved elements in the finite element method, S.I.A.M., J. Numer. Anal., 10, 1973, p. 229-240 and 11, 1974, p. 347-362. | Zbl

Part b: additionat literature

19. R. S. Anderssen, The numerical solution of parabolic differential equations using variational methods, Numer. Math., 13 1969, p. 129-145. | MR | Zbl

20. R. S. Nderssen, A class of densely invertible parabolic operator equations, Bull. Austral Math. Soc, 1, 1969, p. 363-374. | MR | Zbl

21. G. A. Baker, J. Bramble and V. Thomée, Single step Galerkin approximations or parabolic problems, Math. Comp., 31, 1977, p. 818-847. | MR | Zbl

22. W. E. Bosarge Jr., O. G. Johnson and C. L. Smith, A direct method approximation to the linear parabolic regulator problem over multivaraite spline bases, S.I.A.M., J. Numer. Anal, 10, 1973, p. 35-49. | MR | Zbl

23. J. H. Bramble and V. Thomée, Semidiscrete-least squares methods for a parabolic boundary value problem, Math. Comp., 26, 1972,p. 633-648. | MR | Zbl

24. J. Descloux, On the numerical integration of the heat equation, Numer. Math.,15, 1970, p. 371-381. | MR | Zbl

25. J. Douglas Jr., A survey of methods for parabolic differential equations, Advances in Computers, 2, 1961, p. 1-54. | MR | Zbl

26. J. Douglas Jr. and T. Dupont, The numerical solution of waterflooding problems in petroleum engineering by variational methods, Studies in Numer. Anal., 2, 1968, p. 53-63. | MR | Zbl

27. J. Douglas Jr. and T. Dupont, Galerkin methods for parabolic equations, S.I.A.M., J. Numer. Anal., 7, 1970, p. 575-626. | MR | Zbl

28. J. Douglas Jr. and T. Dupont, A finite element collocation method for the heat equation, Symposia Mathematica, 10, 1972, p, 403-410. | MR | Zbl

29. J. Douglas Jr. and T. D Upont, A finite element collocation method for nonlinear parabolic equations, Math. Comp., 27, 1973, p. 17-28. | MR | Zbl

30. J. Douglas Jr. and T. Dupont, Galerkin methods for parabolic equations with nonlinear boundary conditions, Numer. Math., 20, 1973, p. 213-237. | MR | Zbl

31. J. Douglas Jr. and T. Dupont, Collocation methods for parabolic equations in a single space variable (based on C1-piecewise-polynomial spaces), Lecture Notes in Math., 385, 1974. | MR | Zbl

32. J. Douglas Jr., T. Dupont and P. Percell, A time-stepping method for Galerkin approximations for nonlinear parabolic equations (to appear). | MR | Zbl

33. T. Dupont, L2 error estimates for projection methods for parabolic equations in approximating domains, Mathematical aspects of finite elements in partial differential equations, ed. de Boor, Academic Press, New York, 1974, p. 313-352 | MR | Zbl

34. B. A. Finlayson, Convergence of the Galerkin method for nonlinear problems involving chemical reaction, S.I.A.M., J. Numer. Anal., 8, 1971, p. 316-324. | MR | Zbl

35. G. Fix and N. Nassif, On finite element approximation to time dependent problems, Numer. Math., 19, 1972, p. 127-135. | MR | Zbl

36. H. Gajewski and K. Zacharias, Zur starken Konvergenz des Galerkinverfahrens bei einer Klasse pseudo-parabolischer partieller Differentialgleichungen, Math. Nachr., 47, 1970, p. 365-376. | MR | Zbl

37. G. Geymonat and M. Sibony, Approximation de certaines équations paraboliques non linéaires, Calcolo, 13, 1976, p. 213-256. | MR | Zbl

38. H.-P. Helfrich, Fehlerabschätzungen für das Galerkinverfahren zur Lösung von Evolutionsgleichungen, Manuscripta math., 13, 1974, p. 219-235. | MR | Zbl

39. H.-P. Helfrich, Lokale Konvergenz des Galerkinverfahrens bei Gleichungen vom parabolischen Typ in Hilberträumen (to appear).

40. I. Hlavacek, Variational principles for parabolic equations, Api. Mat., 14, 1969, p. 278-297. | MR | Zbl

41. I. Hlavacek, On a semi-variational method for parabolic equations II, Apl. Math., 18, 1973, p. 43-64. | MR | Zbl

42. D. C. Joyce, Survey of extrapolation processes in numerical analysis, S.I.A.M., Rev., 13, 1971, p. 435-490. | MR | Zbl

43. J. T. King, The approximate solution of parabolic initial boundary value problems by weighted least-squares methods, S.I.A.M., J. Numer. Anal., 9, 1972, p. 215-229. | MR | Zbl

44. H. D. Meyer, The numerical solution of nonlinear parabolic problems by variational Methods, S.I.A.M., J. Numer. Anal., 10, 1973, p. 700-722. | MR | Zbl

45. P.A. Raviart, Approximation des équations d'évolution par des méthodes variationnelles, Numer. Anal, of part. diff. equations, éd. J. L. Lions, C.I.M.E., 1968, p. 359-406. | MR

46. P. A. Raviart, The use of numerical integration in finite element methods for solving parabolic equations, Topics in Numer. Anal., éd.J. J. Miller, Academic Press, 1973, p. 233-264. | MR | Zbl

47. R. E. Showalter, A priori error estimates for approximation of parabolic boundary value problems, S.I.A.M., J. Numer. Anal., 12, 1975, p. 456-463. | MR | Zbl

48. P. E. Sobolevsk Ii, The Bubnov-Galerkin method for parabolic equations in Hilbert space, S.M.D., 9, 1968, p. 154-157. | MR | Zbl

49. V. Thomée, Convergence estimates for semi-discrete Galerkin methods for initial value problems, Lecture Notes in Math., 333, 1973, p. 243-262. | MR | Zbl

50. V. Thomée, Some convergence results for Galerkin methods for parabolic boundary value problems, Math. Aspects of Finite Elements in Partial Diff. Equ., ed. C de Boor, Academic Press, New York, 1974, p. 55-88. | MR | Zbl

51. V. Thomée and L. Wahlbin, On Galerkin methods in semilinear parabolic problems, S.I.A.M., J. Numer. Anal., 12, 1975, p. 378-389. | MR | Zbl

52. B. Wendroff, Spline-Galerkin methods for initial value problems with variable coefficients, Lecture Notes in Math., 363, 1974, p. 189-195. | MR | Zbl

53. M. B. Wheeler, An H -1 Galerkin method for parabolic problems in a single space variable, S.I.A.M., J. Numer, Anal., 12, 1975, p. 803-817. | MR | Zbl

54. M. Zlamal, Finite element methods for nonlinear parabolic equations, R.A.I.R.O. Anal. Num., 11, 1977, p. 93-107. | Numdam | MR | Zbl