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 and Continuous Dynamical Systems, 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 and Heterogeneous Media, 2010, 5 (4) : 765-782. doi: 10.3934/nhm.2010.5.765 [2] Adel M. Al-Mahdi, Mohammad M. Al-Gharabli, Mostafa Zahri. Theoretical and computational decay results for a memory type wave equation with variable-exponent nonlinearity. Mathematical Control and Related Fields, 2022  doi: 10.3934/mcrf.2022010 [3] Mohamed Alahyane, Mohammad M. Al-Gharabli, Adel M. Al-Mahdi. Theoretical and computational decay results for a Bresse system with one infinite memory in the longitudinal displacement. Evolution Equations and Control Theory, 2022  doi: 10.3934/eect.2022027 [4] Juan A. Calzada, Rafael Obaya, Ana M. Sanz. Continuous separation for monotone skew-product semiflows: From theoretical to numerical results. Discrete and Continuous Dynamical Systems - B, 2015, 20 (3) : 915-944. doi: 10.3934/dcdsb.2015.20.915 [5] Dorothee Knees, Andreas Schröder. Computational aspects of quasi-static crack propagation. Discrete and Continuous Dynamical Systems - S, 2013, 6 (1) : 63-99. doi: 10.3934/dcdss.2013.6.63 [6] Nicoletta Del Buono, Cinzia Elia, Roberto Garrappa, Alessandro Pugliese. Preface: "Structural Dynamical Systems: Computational aspects". Discrete and Continuous Dynamical Systems - B, 2018, 23 (7) : i-i. doi: 10.3934/dcdsb.201807i [7] Louis Caccetta, Ian Loosen, Volker Rehbock. Computational aspects of the optimal transit path problem. Journal of Industrial and Management Optimization, 2008, 4 (1) : 95-105. doi: 10.3934/jimo.2008.4.95 [8] Simone Göttlich, Oliver Kolb, Sebastian Kühn. Optimization for a special class of traffic flow models: Combinatorial and continuous approaches. Networks and Heterogeneous Media, 2014, 9 (2) : 315-334. doi: 10.3934/nhm.2014.9.315 [9] Nur Aidya Hanum Aizam, Louis Caccetta. Computational models for timetabling problem. Numerical Algebra, Control and Optimization, 2014, 4 (3) : 269-285. doi: 10.3934/naco.2014.4.269 [10] Rolf Bronstering. Some computational aspects of approximate inertial manifolds and finite differences. Discrete and Continuous Dynamical Systems, 1996, 2 (4) : 417-454. doi: 10.3934/dcds.1996.2.417 [11] Yalin Zhang, Guoliang Shi. Continuous dependence of the transmission eigenvalues in one dimension. Inverse Problems and Imaging, 2015, 9 (1) : 273-287. doi: 10.3934/ipi.2015.9.273 [12] Jiří Benedikt. Continuous dependence of eigenvalues of $p$-biharmonic problems on $p$. Communications on Pure and Applied Analysis, 2013, 12 (3) : 1469-1486. doi: 10.3934/cpaa.2013.12.1469 [13] 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 and Applied Analysis, 2014, 13 (1) : 419-433. doi: 10.3934/cpaa.2014.13.419 [14] 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 and Continuous Dynamical Systems - B, 2019, 24 (7) : 3227-3247. doi: 10.3934/dcdsb.2018317 [15] 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 [16] Christophe Chalons. Theoretical and numerical aspects of the interfacial coupling: The scalar Riemann problem and an application to multiphase flows. Networks and Heterogeneous Media, 2010, 5 (3) : 507-524. doi: 10.3934/nhm.2010.5.507 [17] Vladimir Korotkov, Vladimir Emelichev, Yury Nikulin. Multicriteria investment problem with Savage's risk criteria: Theoretical aspects of stability and case study. Journal of Industrial and Management Optimization, 2020, 16 (3) : 1297-1310. doi: 10.3934/jimo.2019003 [18] ShinJa Jeong, Mi-Young Kim. Computational aspects of the multiscale discontinuous Galerkin method for convection-diffusion-reaction problems. Electronic Research Archive, 2021, 29 (2) : 1991-2006. doi: 10.3934/era.2020101 [19] Pavel Krejčí, Thomas Roche. Lipschitz continuous data dependence of sweeping processes in BV spaces. Discrete and Continuous Dynamical Systems - B, 2011, 15 (3) : 637-650. doi: 10.3934/dcdsb.2011.15.637 [20] Ramon Quintanilla. Structural stability and continuous dependence of solutions of thermoelasticity of type III. Discrete and Continuous Dynamical Systems - B, 2001, 1 (4) : 463-470. doi: 10.3934/dcdsb.2001.1.463

2020 Impact Factor: 1.392