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Publikationen


Titel Abstracts Volltext
Reinhardt,H.-J.,
A note on the stability of the upwind scheme for ordinary differential equations.
J. Numer. Math. 20 (2012), 147-158


Reinhardt,H.-J.,
Experimental studies on illposed singularly perturbed boundary value problems for parabolic differential equations.
J. of Physics: Conf. Series 290 (2011) 012013 (10 p.)


Charton, M., Reinhardt,H.-J.,
Method of lines approximations to Cauchy problems for elliptic equations in two dimensions.
Comp. Methods Appl. Mathem. 9(2009), 123-153.


Reinhardt,H.-J., Dinh Nho Hào , Frohne, J., Suttmeier, F.-T.
Numerical solution of Inverse Heat Conduction Problems in two spatial dimensions.
J. Inverse and Ill-Posed Problems 15 (2007), 19-36


Reinhardt,H.-J., Frohne, J., Suttmeier, F.-T., Dinh Nho Hào ,
Multidimensional Inverse Heat Conduction Calculations.
ZAMM (2007), 2 p. (Proc. GAMM Annual Meeting, Berlin 2006)


Charton, M., Reinhardt,H.-J.
Approximation of Cauchy Problems for elliptic equations using the Method of Lines.
WSEAS Transactions on Math. 4, Iss. 2 (2005), 64-69.


Reinhardt,H.-J., Dinh Nho Hào
A Generalization of Beck's Method for Inverse Heat Conduction Problems.
In: Ngoan, H. T. et al. (Hrsg.): ICAAA (International Conference on Abstract and Applied Analysis,
Hanoi, Vietnam, August 2003, 15 S., Kluwer, 2003.


Charton M., Reinhardt, H.-J., Dinh Nho Hào
Numerical Solution of an Elliptic Shape Optimization Problem.
In: D. Petit, D. B. Ingham, Y. Jarny, F. Plourde (Hrsg.):
Inverse Problems and Experimental Design in Thermal and Mechanical Engineering
(Euro Therm 68, F-Poitiers, 5.-7.3.2001), 101 - 107, ENSMA, Poitiers, 2002.


Dinh Nho Hào, Reinhardt,H.-J., Schneider, A.
Numerical Solution to a Sideways Parabolic Equation.
Int. J. Numer. Methods Engin. 50(2001), No. 3, 1253-1267.


Reinhardt,H.-J., Houde Han, Dinh Nho Hào
Stability and Regularization of a Discrete Approximation to the Cauchy Problem for Laplace's equation.
SIAM J. Numer. Anal. 36(1999), No. 3, 890-905.


Dinh Nho Hào, Reinhardt,H.-J.
A Variational Method for Multi-Dimensional Linear Inverse Heat Conduction Problems.
Matimyas Matematika (1998), 48 - 56.

 
Dinh Nho Hào, Reinhardt, H.-J.
Gradient Methods for Inverse Heat Conduction problems.
Inverse Problems in Engineering 6(1998), No. 3, 177-211.

 
Houde Han, Reinhardt, H.-J.
Some stability estimates for Cauchy problems of elliptic equations.
J. Inv. Ill-Posed Problems 5(1997), No. 5, 437-454.

 
Dinh Nho Hào, Reinhardt, H.-J.
On a Sideways Parabolic Equation.
Inverse Problems 13(1997), No. 2, 297-309.


Dinh Nho Hào, Reinhardt, H.-J.
Recent Contributions to Linear Inverse Heat Conduction Problems.
J. Inverse and Ill-posed Problems 4(1997), No. 1, 23-32.

 
Reinhardt, H.-J., Dinh Nho Hào
A Sequential Conjugate Gradient Method for the Stable Numerical Solution
to Inverse Heat Conduction Problems.
Inverse Problems in Engineering 2(1996), 263-272.

 
Dinh Nho Hào, Reinhardt, H.-J.
Stable Numerical Solution to Linear Inverse Heat Conduction by the Conjugate Gradient Method.
J. Inverse and Ill-posed Problems 3(1996), 447-467.

 
Dinh Nho Hào, Schneider, A., Reinhardt, H.-J.
Regularization of a Noncharacteristic Cauchy Problem for a Parabolic Equation.
Inverse Problems 11(1995), No.6, 1247-1263.


Reinhardt, H.-J., Dinh Nho Hào
Efficient Numerical Solution to Inverse Heat Conduction Problems.
In: Wang, K.-W. et al. (Eds.), Design Engineering Techn. Conferences (Boston, 1995),
Vol. 3 - Part C, 917-922. ASME, New York, 1995.

 
Dinh Nho Hào, Reinhardt, H.-J., Schneider, A.
Stable Approximation of Fractional Derivatives of Rough Functions.
BIT 35(1995), 488-503.

 
Reinhardt, H.-J., Dinh Nho Hào
Sequential Approximation to Nonlinear Inverse Heat Conduction Problems.
Math. Computer Modelling 20(1994), No. 10/11, 189-200.

 
Reinhardt, H.-J.
Analysis of the Discrete Beck Method Solving Linear Illposed Parabolic Equations.
Inverse Problems 10(1994), No. 6, 1345-1360.


Dinh Nho Hào, Reinhardt, H.-J.
Towards Linear Inverse Heat Conduction Problems.
E. Lipitakis (Ed.): Proceedings of the HERMIS-Conf. (Athens, 1994), 101-110.
Hellenic Math. Soc., Athens, 1994.

 
Dinh Nho Hào, Reinhardt, H.-J., Seiffarth, F.
Stable Fractional Numerical Differentiation by Mollification.
Numer. Funct. Anal. Optimiz. 15(1994), 635-659.

 
Reinhardt, H.-J., Seiffarth, F.
On the approximate solution of illposed Cauchy problems for parabolic differential equations.
Anger, G. et al. (Hrsg.), Inverse problems: Principles and applications in geophysics, technology and medicine
(Potsdam, 1993), 284-298. Akademie Verlag, Berlin, 1993.
   
Reinhardt, H.-J.
Analysis of sequential methods solving the Inverse Heat Conduction Problem.
Numerical Heat Transfer 24, Part B (1993), 455-474.
   
Reinhardt, H.-J.
A note on discretely compact operators.
Note Math. 12 (1992), 219-227.
   
Reinhardt, H.-J.
A numerical method for the solution of two-dimensional inverse heat conduction problems.
Internat. J. Numer. Methods Engrg. 32 (1991), 363-383.
   
Baumeister J., Reinhardt, H.-J.
On the approximate solution of a two-dimensional inverse heat conduction problem.
Engl, H. W., Groetsch, C. W. (Hrsg.), Inverse and ill-posed problems
(St. Wolfgang, 1986), 325-344. Academic Press, 1987.
   
Reinhardt, H.-J.
A-posteriori error estimation for finite element modifications of line methods applied to singularly perturbed partial
differential equations.
Appl. Numer. Math. 1 (1985), 145-176.
   
Reinhardt, H.-J.
On a principle of direct defect correction based on a-posteriori error estimates.
Böhmer, K., Stetter, H. J. (Hrsg.), Defect correction methods.
Theory and Applications (Oberwolfach, 1983). Computing Suppl. 5 (1984), 43-66.
   
Reinhardt, H.-J.
Defect corrections with finite element methods for singular perturbation problems.
Miller, J. J. H. (Hrsg.), Computational and asymptotic methods for boundary and interior layers
(BAIL II, Dublin, 1982), 348-352. Boole, Dublin, 1982.
   
Reinhardt, H.-J.
Defect correction and asymptotic expansions for the approximate solution
of functional equations containing a small parameter.
I. Basic perturbation theory.
II. Asymptotic expansions for a singular perturbation problem.
Miller, J. J. H. (Hrsg.), An introduction to computational
and asymptotic methods for boundary and interior layers
(BAIL II Short Cours, Dublin, 1982), 88-99. Boole, Dublin,1982.
   
Reinhardt, H.-J.
Analysis of adaptive finite element methods for - \varepsilon u" + u' = f based on a-posteriori error estimates.
Eckhaus, W., de Jager, E. M. (Hrsg.),
Theory and applications of singular perturbations
(Oberwolfach, 1981), 207-227. LNM, Vol. 942. Springer, 1982.
   
Reinhardt, H.-J.
A-posteriori error analysis and adaptive finite element methods for singularly perturbed
convection-diffusion equations.
Math. Methods Appl. Sci. 4 (1982), 529-548.
   
Reinhardt, H.-J.
A-posteriori error estimation and adaptive finite element computations for singularly perturbed one space
dimensional parabolic equations.
Axelsson, O., Frank, L. S., van der Sluis, A. (Hrsg.),
Analytical and numerical approaches to asymptotic problems in analysis (Nijmegen, 1980), 213-233. North-Holland, 1981.
   
Reinhardt, H.-J.
A-posteriori error estimates for the finite element solution
of a singularly perturbed linear ordinary differential equation.
SIAM J. Numer. Anal. 18 (1981), 406-430.
   
Reinhardt, H.-J.
Singular perturbations of difference methods
for linear ordinary differential equations.
Appl. Anal. 10 (1980), 53-70.
   
Reinhardt, H.-J.
On asymptotic expansions in nonlinear, singularly perturbed difference equations.
Numer. Funct. Anal. Optim. 1 (1979), 565-587.
   
Reinhardt, H.-J.
Stability of singularly perturbed linear difference equations.
Hemker, P. W., Miller, J. J. H. (Hrsg.),
Numerical analysis of singular perturbation problems.
(Nijmegen, 1978), 485-492. Academic Press, London, 1979.
   
Reinhardt, H.-J.
Differentiable difference approximations for nonlinear initial-value problems II.
Appl. Anal. 7 (1978), 81-96.
   
Reinhardt, H.-J.
Differentiable difference approximations for nonlinear initial-value problems I.
Appl. Anal. 6 (1977), 281-298.
   
Reinhardt, H.-J.
On the existence of generalized solutions and the convergence of difference methods of nonlinear initial-value problems.
Manuscripta Math. 17 (1975), 151-170.
   
Reinhardt, H.-J.
Nonlinear mappings in metric discrete limit spaces and their topological properties.
Collect. Math. 26 (1975), 173-204.
   
Stummel, F., Reinhardt, H.-J.
Discrete convergence of continuous mappings in metric spaces.
Ansorge, R., Törnig, W. (Hrsg.),
Numerische, insbesondere approximationstheoretische Behandlung von Funktionalgleichungen
(Oberwolfach, 1972), 218-242. LNM, Vol. 333. Springer, Berlin, 1973.
   
Bücher

   
Reinhardt, H.-J.
Numerik gewöhnlicher Differentialgleichungen. Anfangs- und Randwertprobleme. (297 Seiten)
2. Auflage, De Gruyter, Berlin 2012.
   
Reinhardt, H.-J.
Analysis of approximation methods for differential and integral equations. (398 Seiten)
Appl. Math. Sc. Vol. 57, Springer, New York, 1985
   
     

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reinhardt@mathematik.uni-siegen.de