Vuik, C.; Cuvelier, C. Numerical solution of an etching problem. (English) Zbl 0586.65085 J. Comput. Phys. 59, 247-263 (1985). After a short description of the chemical background of etching processes, a simplified mathematical model is formulated. This contains two parameters that determine the etching profile. Two approaches for obtaining a numerical solution are discussed. First, the problem in terms of a variational inequality is reformulated and some new results on its numerical solution are presented. Then, how the problem can be solved by means of a moving grid method as well is explored. Results obtained by both methods are presented and compared. The latter method is applicable to a much wider class of boundary conditions, but the variational inequality approach seems attractive for other reasons. Finally this work is compared with some experimental results. Cited in 10 Documents MSC: 65Z05 Applications to the sciences 65N22 Numerical solution of discretized equations for boundary value problems involving PDEs 35K05 Heat equation 80A30 Chemical kinetics in thermodynamics and heat transfer 49J40 Variational inequalities 65K10 Numerical optimization and variational techniques Keywords:wet chemical etching; variational inequality; moving grid method PDFBibTeX XMLCite \textit{C. Vuik} and \textit{C. Cuvelier}, J. Comput. Phys. 59, 247--263 (1985; Zbl 0586.65085) Full Text: DOI References: [1] Allen, D. M.; Horne, D. F.; Stevens, G. W.W., J. Photogr. Sci., 25, 254 (1977) [2] Allen, D. M.; Horne, D. F.; Stevens, G. W.W., J. Photogr. Sci., 26, 242 (1978) [3] Yanagawa, T.; Takekoshi, I., IEEE Trans. Electron. Devices, 17, 964 (1970) [4] C. Vuik; C. Vuik [5] Ockendon, J. R.; Hodgkins, W. R., Moving Boundary Problems in Heat Flow and Diffusion (1975), Oxford Univ. Press (Clarendon): Oxford Univ. Press (Clarendon) Oxford · Zbl 0295.76064 [6] Thirsk, H. R.; Harrison, J. A., A guide to the Study of Electrode Kinetics (1972), Academic Press: Academic Press New York/London [7] Pamplin, B. R., Crystal Growth (1975), Pergamon: Pergamon Oxford [8] Cryer, C. W., A Survey of Trial Free Boundary Methods for the Numerical Solution of Free Boundary Problems, MRC Tech. Summ. Rep. 1693 (1976) [9] Elliott, C. M.; Ockendon, J. R., Weak and Variational Methods for Moving Boundary Problems (1982), Pitman: Pitman Boston · Zbl 0476.35080 [10] Fasano, A.; Primicerio, M., Free Boundary Problems: Theory and Applications (1983), Pitman: Pitman Boston [11] Lions, J. L., Introduction to some aspects of free surface problems, (Hubbard, B., Numerical Solution of Partial Differential Equations (1976), Academic Press: Academic Press New York) · Zbl 0338.65053 [12] Baiocchi, C., Ann. Mat. Pure Appl., 98, 1 (1973) [13] Duvaut, G., C. R. Acad. Sci. Paris, 276, 1461 (1973) [14] Lions, J. L., Quelques méthodes de resolution des probéms aux limites non linéaires (1969), Dunod: Dunod Paris · Zbl 0189.40603 [15] Glowinski, R.; Lions, J. L.; Trémolières, R., Numerical Analysis of Variational Inequalities (1980), North-Holland: North-Holland Amsterdam · Zbl 0508.65029 [16] Cryer, C. W., SIAM J. Control, 9, 385 (1971) [17] Varga, R. S., Matrix Iterative Analysis (1962), Prentice-Hall: Prentice-Hall London · Zbl 0133.08602 [18] Carré, B. A., Comput. J., 4, 73 (1961) [19] Murray, W. D.; Landis, F., Trans. ASME J. Heat Transfer, 81, 106 (1959) [20] Santos, V. R.B., Comp. Methods Appl. Mech. Eng., 25, 51 (1981) [21] Lynch, D. R.; O’Neill, K., Int. J. Numer. Methods Eng., 17, 81 (1981) [22] Babuska, I.; Azlz, A. K., SIAM J. Numer. Anal., 13, 214 (1976) [23] Bonnerot, R.; Jamet, P., J. Comput. Phys., 25, 163 (1977) [24] Kuiken, H. K., (Proc. Roy. Soc. London. Ser. A, 39b (1984)), 95 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.