# American Institute of Mathematical Sciences

January  1996, 2(1): 141-149. doi: 10.3934/dcds.1996.2.141

## On continuous dependence under approximation for groundwater flow models with distributed and pointwise observations

 1 CRSC & Department of Mathematics, North Carolina State University, Raleigh, NC 27695-8205, United States, United States

Received  July 1995 Published  October 1995

We present in this paper some results on continuous dependence for parameters in a groundwater flow model. These results are crucial for theoretical and computational aspects of least squares estimation of parameters. As is typically the case in field studies, the form of the data is pointwise observation of hydraulic head and hydraulic conductivity at a discrete collection of observation well sites. We prove continuous dependence results for the solution of the groundwater flow equation, with respect to conductivity and boundary values, under certain types of numerical approximation.
Citation: B.G. Fitzpatrick, M.A. Jeffris. On continuous dependence under approximation for groundwater flow models with distributed and pointwise observations. Discrete & Continuous Dynamical Systems - A, 1996, 2 (1) : 141-149. doi: 10.3934/dcds.1996.2.141
 [1] Michiel Bertsch, Carlo Nitsch. Groundwater flow in a fissurised porous stratum. Networks & Heterogeneous Media, 2010, 5 (4) : 765-782. doi: 10.3934/nhm.2010.5.765 [2] Juan A. Calzada, Rafael Obaya, Ana M. Sanz. Continuous separation for monotone skew-product semiflows: From theoretical to numerical results. Discrete & Continuous Dynamical Systems - B, 2015, 20 (3) : 915-944. doi: 10.3934/dcdsb.2015.20.915 [3] Dorothee Knees, Andreas Schröder. Computational aspects of quasi-static crack propagation. Discrete & Continuous Dynamical Systems - S, 2013, 6 (1) : 63-99. doi: 10.3934/dcdss.2013.6.63 [4] Nicoletta Del Buono, Cinzia Elia, Roberto Garrappa, Alessandro Pugliese. Preface: "Structural Dynamical Systems: Computational aspects". Discrete & Continuous Dynamical Systems - B, 2018, 23 (7) : i-i. doi: 10.3934/dcdsb.201807i [5] Louis Caccetta, Ian Loosen, Volker Rehbock. Computational aspects of the optimal transit path problem. Journal of Industrial & Management Optimization, 2008, 4 (1) : 95-105. doi: 10.3934/jimo.2008.4.95 [6] Nur Aidya Hanum Aizam, Louis Caccetta. Computational models for timetabling problem. Numerical Algebra, Control & Optimization, 2014, 4 (3) : 269-285. doi: 10.3934/naco.2014.4.269 [7] Simone Göttlich, Oliver Kolb, Sebastian Kühn. Optimization for a special class of traffic flow models: Combinatorial and continuous approaches. Networks & Heterogeneous Media, 2014, 9 (2) : 315-334. doi: 10.3934/nhm.2014.9.315 [8] Rolf Bronstering. Some computational aspects of approximate inertial manifolds and finite differences. Discrete & Continuous Dynamical Systems - A, 1996, 2 (4) : 417-454. doi: 10.3934/dcds.1996.2.417 [9] Yalin Zhang, Guoliang Shi. Continuous dependence of the transmission eigenvalues in one dimension. Inverse Problems & Imaging, 2015, 9 (1) : 273-287. doi: 10.3934/ipi.2015.9.273 [10] Jiří Benedikt. Continuous dependence of eigenvalues of $p$-biharmonic problems on $p$. Communications on Pure & Applied Analysis, 2013, 12 (3) : 1469-1486. doi: 10.3934/cpaa.2013.12.1469 [11] Giuseppe Maria Coclite, Angelo Favini, Gisèle Ruiz Goldstein, Jerome A. Goldstein, Silvia Romanelli. Continuous dependence in hyperbolic problems with Wentzell boundary conditions. Communications on Pure & Applied Analysis, 2014, 13 (1) : 419-433. doi: 10.3934/cpaa.2014.13.419 [12] Christophe Chalons. Theoretical and numerical aspects of the interfacial coupling: The scalar Riemann problem and an application to multiphase flows. Networks & Heterogeneous Media, 2010, 5 (3) : 507-524. doi: 10.3934/nhm.2010.5.507 [13] Vladimir Korotkov, Vladimir Emelichev, Yury Nikulin. Multicriteria investment problem with Savage's risk criteria: Theoretical aspects of stability and case study. Journal of Industrial & Management Optimization, 2020, 16 (3) : 1297-1310. doi: 10.3934/jimo.2019003 [14] Juvencio Alberto Betancourt-Mar, Víctor Alfonso Méndez-Guerrero, Carlos Hernández-Rodríguez, José Manuel Nieto-Villar. Theoretical models for chronotherapy: Periodic perturbations in hyperchaos. Mathematical Biosciences & Engineering, 2010, 7 (3) : 553-560. doi: 10.3934/mbe.2010.7.553 [15] Pierre Aime Feulefack, Jean Daniel Djida, Atangana Abdon. A new model of groundwater flow within an unconfined aquifer: Application of Caputo-Fabrizio fractional derivative. Discrete & Continuous Dynamical Systems - B, 2019, 24 (7) : 3227-3247. doi: 10.3934/dcdsb.2018317 [16] Rafał Kamocki, Marek Majewski. On the continuous dependence of solutions to a fractional Dirichlet problem. The case of saddle points. Discrete & Continuous Dynamical Systems - B, 2014, 19 (8) : 2557-2568. doi: 10.3934/dcdsb.2014.19.2557 [17] Pavel Krejčí, Thomas Roche. Lipschitz continuous data dependence of sweeping processes in BV spaces. Discrete & Continuous Dynamical Systems - B, 2011, 15 (3) : 637-650. doi: 10.3934/dcdsb.2011.15.637 [18] Ramon Quintanilla. Structural stability and continuous dependence of solutions of thermoelasticity of type III. Discrete & Continuous Dynamical Systems - B, 2001, 1 (4) : 463-470. doi: 10.3934/dcdsb.2001.1.463 [19] P.E. Kloeden, Pedro Marín-Rubio. Equi-Attraction and the continuous dependence of attractors on time delays. Discrete & Continuous Dynamical Systems - B, 2008, 9 (3&4, May) : 581-593. doi: 10.3934/dcdsb.2008.9.581 [20] Paola Goatin, Philippe G. LeFloch. $L^1$ continuous dependence for the Euler equations of compressible fluids dynamics. Communications on Pure & Applied Analysis, 2003, 2 (1) : 107-137. doi: 10.3934/cpaa.2003.2.107

2019 Impact Factor: 1.338