Steady filtration problems with seawater intrusion: macro-hybrid primal mixed variational analysis

References

• Alduncin , G and Esquivel-Avila , J . 2000 . Steady filtration problems with seawater intrusion: Penalized finite element approximations . Comput. Methods Appl. Mech. Eng. , 190 : 609 – 624 .
   Google Scholar
• Alduncin , G , Esquivel-Avila , J and Reyes-Avila , L . 1998 . Steady filtration problems with seawater intrusion: Variational analysis . Comput. Methods Appl. Mech. Eng. , 151 : 13 – 25 .
   Google Scholar
• Brezis , H , Kinderlehrer , D and Stampacchia , G . 1978 . Sur une nouvelle formulation du problème de l'écoulement à travers une digue . C.R. Acad. Sci. Paris Série A , 287 : 711 – 714 .
   Google Scholar
• Alt , HW . 1977 . Free boundary problem associated with the flow of ground water . Arch. Rat. Mech. Anal. , 64 : 111 – 126 .
   Google Scholar
• Alt , HW . 1979 . Strömungen durch inhomogene poröse medien mit freiem rand . J. Reine Angew. Math. , 305 : 89 – 115 .
   Google Scholar
• Carrillo-Menendez , J and Chipot , M . 1982 . On the dam problem . J. Diff. Equ. , 45 : 234 – 271 .
   Google Scholar
• Chipot , M . 1984 . Variational Inequalities and Flow in Porous Media , New York : Springer-Verlag .
   Google Scholar
• Alt , HW . 1980 . Numerical solution of steady-state porous flow free boundary problems . Numer. Math. , 36 : 73 – 98 .
   Web of Science ®Google Scholar
• Pietra , P . 1982 . An up-wind finite element method for a filtration problem . RAIRO Anal. Numér. , 16 : 463 – 481 .
   Google Scholar
• Marini , LD and Pietra , P . 1986 . Fixed-point algorithms for stationary flow in porous media . Comput. Methods Appl. Mech. Eng. , 56 : 17 – 45 .
   Google Scholar
• Baiocchi , C , Comincioli , V , Magenes , E and Pozzi , GA . 1973 . Free boundary problems in the theory of fluid flow through porous media: Existence and uniqueness theorems . Ann. Mat. Pura Appl. , 4 : 1 – 82 .
   Google Scholar
• Baiocchi , C , Comincioli , V , Guerri , L and Volpi , G . 1973 . Free boundary problems in the theory of fluid flow through porous media: A numerical approach . Calcolo , 10 : 1 – 85 .
   Google Scholar
• Baiocchi , C and Capelo , A . 1984 . Variational and Quasivariational Inequalities: Applications to Free Boundary Problems , Chichester : Wiley .
   Google Scholar
• Oden , JT and Kikuchi , N . 1984 . Recent advances: Theory of variational inequalities with applications to problems of flow through porous media . Int. J. Eng. Sci. , 18 : 1173 – 1284 .
   Google Scholar
• Alduncin , G , Esquivel-Avila , J and Vera-Guzman , N . 2005 . Steady filtration problems with seawater intrusion: Macro-hybrid penalized finite element approximations . Int. J. Numer. Methods Fluids , 49 : 935 – 957 .
   Google Scholar
• Alduncin , G . 2005 . Composition duality principles for mixed variational inequalities . Math. Comput. Modelling , 41 : 639 – 654 .
   Google Scholar
• Alduncin , G . 2005 . Composition duality methods for mixed variational inclusions . Appl. Math. Optim. , 52 : 311 – 348 .
   Web of Science ®Google Scholar
• Ciarlet , PG . 1991 . “ Basic error estimates for elliptic problems ” . In Handbook of Numerical Analysis, Vol. 2, Finite Element Methods (Part 1) , Edited by: Ciarlet , PG and Lions , JL . 17 – 351 . Amsterdam : North-Holland .
   Google Scholar
• Raviart , PA and Thomas , J-M . 1977 . Primal hybrid finite element methods for 2nd order elliptic equations . Math. Comp. , 31 : 391 – 413 .
   Web of Science ®Google Scholar
• Brezzi , F and Fortin , M . 1991 . Mixed and Hybrid Finite Element Methods , New York : Springer-Verlag .
   Google Scholar
• Roberts , JE and Thomas , J-M . 1991 . “ Mixed and hybrid methods ” . In Handbook of Numerical Analysis , Edited by: Ciarlet , PG and Lions , JL . 523 – 639 . Amsterdam : North-Holland .
   Google Scholar
• Tabata , M . 1978 . Uniform convergence of the upwind finite element approximation for semilinear parabolic problems . J. Math. Kyoto Univ. , 18 : 327 – 351 .
   Google Scholar
• Alduncin , G . 1996 . Numerical resolvent methods for constrained problems in mechanics . Approx. Theory Appl. , 12 ( 4 ) : 1 – 25 .
   Google Scholar
• Alduncin , G . 1998 . Numerical resolvent methods for macro-hybrid mixed variational inequalities . Numer. Funct. Anal. Optimiz. , 19 : 667 – 696 .
   Web of Science ®Google Scholar
• Alduncin , G . 2003 . “ Parallel proximal-point algorithms for constrained problems in mechanics ” . In Practical Applications of Parallel Computing , Edited by: Yang , LT and Paprzycki , M . 69 – 88 . New York : Nova Science .
   Google Scholar
• Alduncin , G . 1997 . On Gabay's algorithms for mixed variational inequalities . Appl. Math. Optim. , 35 : 21 – 44 .
   Web of Science ®Google Scholar
• Alduncin , G . 2007 . Macro-hybrid variational formulations of constrained boundary value problems . Numer. Funct. Anal. Optimiz. , 28 : 751 – 774 .
   Web of Science ®Google Scholar