The paper is concerned with the study of a parabolic initial-boundary value problem with nonlinear Newton boundary condition considered in a two-dimensional domain. The goal is to prove the existence and uniqueness of a weak solution to the problem in the case when the nonlinearity in the Newton boundary condition does not satisfy any monotonicity condition and to analyze the finite element approximation.
@article{119333,
author = {Miloslav Feistauer and Karel Najzar and Karel \v Svadlenka},
title = {On a parabolic problem with nonlinear Newton boundary conditions},
journal = {Commentationes Mathematicae Universitatis Carolinae},
volume = {43},
year = {2002},
pages = {429-455},
zbl = {1090.35102},
mrnumber = {1920519},
language = {en},
url = {http://dml.mathdoc.fr/item/119333}
}
Feistauer, Miloslav; Najzar, Karel; Švadlenka, Karel. On a parabolic problem with nonlinear Newton boundary conditions. Commentationes Mathematicae Universitatis Carolinae, Tome 43 (2002) pp. 429-455. http://gdmltest.u-ga.fr/item/119333/
Soil Nutrient Bioavailability: A Mechanistic Approach, John Wiley & Sons, Inc., New York, 1995.
Boundary value problems in heat conduction with nonlinear material and nonlinear boundary conditions, Appl. Math. Model. 5 (1981), 417-421. (1981) | Zbl 0475.65078
The Mathematical Theory of Finite Element Methods, Springer, New York, 1994. | MR 1278258 | Zbl 1135.65042
Finite element error estimates for nonlinear elliptic equations of monotone type, Numer. Math. 54 (1989), 373-393. (1989) | MR 0972416
The Finite Element Method for Elliptic Problems, North Holland, Amsterdam, 1978. | MR 0520174 | Zbl 0547.65072
The combined effect of curved boundaries and numerical integration in isoparametric finite element method, in: The Mathematical Foundations of the Finite Element Method with Application to Partial Differential Equations (A.K. Aziz, Ed.), Academic Press, New York, 1972. | MR 0421108
Simulation model for nutrient uptake from soil by a growing plant root system, Agronomy Journal 68 (1976), 961-964. (1976)
Real and complex interpolation and extrapolation of compact operators, Duke Math. J. 65.2 (1992), 333-343. (1992) | MR 1150590 | Zbl 0787.46062
A finite volume discontinuous Galerkin scheme for nonlinear convection-diffusion problems, preprint, Forschungsinstitut für Mathematik, ETH Zürich, January 2001 (to appear in Calcolo). | MR 1901200
Mathematical Methods in Fluid Mechanics, The Pitman Monographs and Surveys in Pure and Applied Mathematics 67, Longman Scientific and Technical Series, Harlow, 1993. | MR 1266627
Mathematical modelling of an electrolysis process, Comment Math. Univ. Carolinae 30 (1989), 465-477. (1989) | MR 1031864 | Zbl 0704.35021
Finite element approximation of a problem with a nonlinear Newton boundary condition, Numer. Math. 78 (1998), 403-425. (1998) | MR 1603350 | Zbl 0888.65118
Error estimates for the finite element solution of elliptic problems with nonlinear Newton boundary conditions, Numer. Funct. Anal. Optim. 20 (1999), 835-851. (1999) | MR 1728186
On the finite element analysis of problems with nonlinear Newton boundary conditions in nonpolygonal domains, Appl. Math. 46 (2001), 353-382. (2001) | MR 1925193 | Zbl 1066.65124
Numerical analysis of problems with nonlinear Newton boundary conditions, in: Proc. of the 3rd European Conference Numerical Mathematics and Advanced Applications (P. Neittaanmäki, T. Tiihonen, P. Tarvainen, Editors), World Scientific, Singapore, 2000, pp.486-493.
Finite element approximation of nonlinear elliptic problems with discontinuous coefficients, M$^{2}$AN 24 (1990), 457-500. (1990) | MR 1070966
Finite element solution of nonlinear elliptic problems, Numer. Math. 50 (1987), 451-475. (1987) | MR 0875168
A pseudospectral three-dimensional boundary integral method applied to a nonlinear model problem from finite elasticity, SIAM J. Numer. Anal. 31 (1994), 1378-1414. (1994) | MR 1293521 | Zbl 0815.41008
Boundary element methods for potential problems with nonlinear boundary conditions, Applied Mathematics Report AMR98/17, School of Mathematics, The University of New South Wales, Sydney, 1998. | Zbl 0971.65107
Nonlinear boundary integral equations for harmonic problems, Applied Mathematics Report AMR98/20, School of Mathematics, The University of New South Wales, Sydney, 1998. | MR 1738277 | Zbl 0974.65112
Finite Element Approximation of the Navier-Stokes Equations, Lecture Notes in Mathematics 749, Springer-Verlag, Berlin-Heidelberg-New York, 1979. | MR 0548867 | Zbl 0441.65081
Finite element analysis of a nonlinear elliptic problem with a pure radiation condition, in: Applied Nonlinear Analysis, Kluwer, Amsterdam, 1999, pp.271-280. | MR 1727454
Function Spaces, Academia, Prague, 1977. | MR 0482102
Ordinary Differential Equations, Elsevier, Amsterdam-Oxford-New York-Tokyo, 1986. | MR 0929466 | Zbl 0756.34003
Quelques méthodes de résolution des problémes aux limites non linéaires, Dunod, Paris, 1969. | MR 0259693 | Zbl 0248.35001
Problémes aux limites non homogénes et applications, Dunod, Paris, 1968. | Zbl 0212.43801
Finite element analysis of a radiation heat transfer problem, J. Comput. Math. 16 (1998), 327-336. (1998)
Weak and Measure-Valued Solutions to Evolutionary PDEs, Chapman & Hall, London, 1996. | MR 1409366
An analysis of the hydrodynamics of aluminium reduction cells, J. Electrochem. Soc. 31 (1984), 2251-2259. (1984)
Les méthodes directes en théories des équations elliptiques, Academia, Prague, 1967. | MR 0227584
Higher order finite element method for a problem with nonlinear boundary condition, in: Proc. of the 13th Summer School ``Software and Algorithms of Numerical Mathematics'', West Bohemian University Pilsen, 1999, pp.301-308.
Navier-Stokes Equations, North-Holland, Amsterdam-New York-Oxford, 1977. | MR 0603444 | Zbl 1157.35333
Nonhomogeneous boundary conditions and curved triangular finite elements, Appl. Math. 26 (1981), 121-141. (1981) | MR 0612669
The finite element method for nonlinear elliptic equations with discontinuous coefficients, Numer. Math. 58 (1990), 51-77. (1990) | MR 1069653
Curved elements in the finite element method, I. SIAM J. Numer. Anal. 10 (1973), 229-240. (1973) | MR 0395263