Academic Journal
On a parabolic problem with nonlinear Newton boundary conditions
| العنوان: | On a parabolic problem with nonlinear Newton boundary conditions |
|---|---|
| المؤلفون: | Feistauer, Miloslav, Najzar, Karel, Švadlenka, Karel |
| بيانات النشر: | Charles University in Prague, Faculty of Mathematics and Physics |
| سنة النشر: | 2002 |
| المجموعة: | DML-CZ (Czech Digital Mathematics Library) |
| مصطلحات موضوعية: | keyword:parabolic convection-diffusion equation, keyword:nonlinear Newton boundary condition, keyword:Galerkin method, keyword:compactness method, keyword:finite element approximation, keyword:error estimates, msc:35A35, msc:35D05, msc:35K57, msc:35K60, msc:65M60, msc:65N15, msc:65N30 |
| الوصف: | summary: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. |
| نوع الوثيقة: | text |
| وصف الملف: | application/pdf |
| اللغة: | English |
| تدمد: | 0010-2628 1213-7243 |
| Relation: | mr:MR1920519; zbl:Zbl 1090.35102; reference:[1] Barber S.A.: Soil Nutrient Bioavailability: A Mechanistic Approach.John Wiley & Sons, Inc., New York, 1995.; reference:[2] Bialecki R., Nowak A.J.: Boundary value problems in heat conduction with nonlinear material and nonlinear boundary conditions.Appl. Math. Model. 5 (1981), 417-421. Zbl 0475.65078; reference:[3] Brenner S.C., Scott L.R.: The Mathematical Theory of Finite Element Methods.Springer, New York, 1994. Zbl 1135.65042, MR 1278258; reference:[4] Chow S.S.: Finite element error estimates for nonlinear elliptic equations of monotone type.Numer. Math. 54 (1989), 373-393. MR 0972416; reference:[5] Ciarlet P.G.: The Finite Element Method for Elliptic Problems.North Holland, Amsterdam, 1978. Zbl 0547.65072, MR 0520174; reference:[6] Ciarlet P.G., Raviart P.A.: 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; reference:[7] Claassen N., Barber S.A.: Simulation model for nutrient uptake from soil by a growing plant root system.Agronomy Journal 68 (1976), 961-964.; reference:[8] Cwikel M.: Real and complex interpolation and extrapolation of compact operators.Duke Math. J. 65.2 (1992), 333-343. Zbl 0787.46062, MR 1150590; reference:[9] Dolejší V., Feistauer M., Schwab C.: 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; reference:[10] Feistauer M.: 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; reference:[11] Feistauer M., Kalis H., Rokyta M.: Mathematical modelling of an electrolysis process.Comment Math. Univ. Carolinae 30 (1989), 465-477. Zbl 0704.35021, MR 1031864; reference:[12] Feistauer M., Najzar K.: Finite element approximation of a problem with a nonlinear Newton boundary condition.Numer. Math. 78 (1998), 403-425. Zbl 0888.65118, MR 1603350; reference:[13] Feistauer M., Najzar K., Sobotíková V.: Error estimates for the finite element solution of elliptic problems with nonlinear Newton boundary conditions.Numer. Funct. Anal. Optim. 20 (1999), 835-851. MR 1728186; reference:[14] Feistauer M., Najzar K., Sobotíková V.: On the finite element analysis of problems with nonlinear Newton boundary conditions in nonpolygonal domains.Appl. Math. 46 (2001), 353-382. Zbl 1066.65124, MR 1925193; reference:[15] Feistauer M., Najzar K., Sobotíková V., Sváček P.: 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.; reference:[16] Feistauer M., Sobotíková V.: Finite element approximation of nonlinear elliptic problems with discontinuous coefficients.M$^{2}$AN 24 (1990), 457-500. MR 1070966; reference:[17] Feistauer M., Ženíšek A.: Finite element solution of nonlinear elliptic problems.Numer. Math. 50 (1987), 451-475. MR 0875168; reference:[18] Ganesh M., Graham I.G., Sivaloganathan J.: A pseudospectral three-dimensional boundary integral method applied to a nonlinear model problem from finite elasticity.SIAM J. Numer. Anal. 31 (1994), 1378-1414. Zbl 0815.41008, MR 1293521; reference:[19] Ganesh M., Steinbach O.: 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; reference:[20] Ganesh M., Steinbach O.: Nonlinear boundary integral equations for harmonic problems.Applied Mathematics Report AMR98/20, School of Mathematics, The University of New South Wales, Sydney, 1998. Zbl 0974.65112, MR 1738277; reference:[21] Girault V., Raviart P.A.: Finite Element Approximation of the Navier-Stokes Equations.Lecture Notes in Mathematics 749, Springer-Verlag, Berlin-Heidelberg-New York, 1979. Zbl 0441.65081, MR 0548867; reference:[22] Křížek M., Liu L., Neittaanmäki P.: 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; reference:[23] Kufner A., John O., Fučík S.: Function Spaces.Academia, Prague, 1977. MR 0482102; reference:[24] Kurzweil J.: Ordinary Differential Equations.Elsevier, Amsterdam-Oxford-New York-Tokyo, 1986. Zbl 0756.34003, MR 0929466; reference:[25] Lions J.L.: Quelques méthodes de résolution des problémes aux limites non linéaires.Dunod, Paris, 1969. Zbl 0248.35001, MR 0259693; reference:[26] Lions J.L., Magenes E.: Problémes aux limites non homogénes et applications.Dunod, Paris, 1968. Zbl 0212.43801; reference:[27] Liu L., Křížek M.: Finite element analysis of a radiation heat transfer problem.J. Comput. Math. 16 (1998), 327-336.; reference:[28] Málek J., Nečas J., Rokyta M., Růžička M.: Weak and Measure-Valued Solutions to Evolutionary PDEs.Chapman & Hall, London, 1996. MR 1409366; reference:[29] Moreau R., Ewans J.W.: An analysis of the hydrodynamics of aluminium reduction cells.J. Electrochem. Soc. 31 (1984), 2251-2259.; reference:[30] Nečas J.: Les méthodes directes en théories des équations elliptiques.Academia, Prague, 1967. MR 0227584; reference:[31] Sváček P.: 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.; reference:[32] Temam R.: Navier-Stokes Equations.North-Holland, Amsterdam-New York-Oxford, 1977. Zbl 1157.35333, MR 0603444; reference:[33] Ženíšek A.: Nonhomogeneous boundary conditions and curved triangular finite elements.Appl. Math. 26 (1981), 121-141. MR 0612669; reference:[34] Ženíšek A.: The finite element method for nonlinear elliptic equations with discontinuous coefficients.Numer. Math. 58 (1990), 51-77. MR 1069653; reference:[35] Zlámal M.: Curved elements in the finite element method.I. SIAM J. Numer. Anal. 10 (1973), 229-240. MR 0395263 |
| الاتاحة: | http://hdl.handle.net/10338.dmlcz/119333 |
| Rights: | access:Unrestricted ; rights:DML-CZ Czech Digital Mathematics Library, http://dml.cz/ ; rights:Institute of Mathematics AS CR, http://www.math.cas.cz/ ; conditionOfUse:http://dml.cz/use |
| رقم الانضمام: | edsbas.D219960A |
| قاعدة البيانات: | BASE |
| تدمد: | 00102628 12137243 |
|---|