Weak Galerkin method for the Biot’s consolidation model

Hu, Xiaozhe; Mu, Lin; Ye, Xiu

doi:10.1016/j.camwa.2017.07.013

Weak Galerkin method for the Biot’s consolidation model

Journal Article · Thu Mar 01 00:00:00 EST 2018 · Computers and Mathematics with Applications (Oxford)

DOI:https://doi.org/10.1016/j.camwa.2017.07.013· OSTI ID:1854979

Hu, Xiaozhe; Mu, Lin; Ye, Xiu

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Research Organization:: Oak Ridge National Laboratory (ORNL), Oak Ridge, TN (United States)

Sponsoring Organization:: USDOE Office of Science (SC), Advanced Scientific Computing Research (ASCR); USDOE Office of Science (SC), Advanced Scientific Computing Research (ASCR) (SC-21)

Grant/Contract Number:: AC05-00OR22725

OSTI ID:: 1854979

Alternate ID(s):: OSTI ID: 1582708
OSTI ID: 1394349

Journal Information:: Computers and Mathematics with Applications (Oxford), Journal Name: Computers and Mathematics with Applications (Oxford) Journal Issue: 6 Vol. 75; ISSN 0898-1221

Publisher:: ElsevierCopyright Statement

Country of Publication:: United Kingdom

Language:: English

References (40)

Coupling temperature to a double-porosity model of deformable porous media Masters, I.; Pao, W. K. S.; Lewis, R. W. International Journal for Numerical Methods in Engineering, Vol. 49, Issue 3 https://doi.org/10.1002/1097-0207(20000930)49:3<421::AID-NME48>3.0.CO;2-6	journal	January 2000
On the causes of pressure oscillations in low-permeable and low-compressible porous media: PRESSURE OSCILLATIONS IN LOW-PERMEABLE POROUS MEDIA Haga, Joachim Berdal; Osnes, Harald; Langtangen, Hans Petter International Journal for Numerical and Analytical Methods in Geomechanics, Vol. 36, Issue 12 https://doi.org/10.1002/nag.1062	journal	July 2011
Numerical simulation of secondary consolidation of soil: Finite element application Lewis, R. W.; Tran, D. V. International Journal for Numerical and Analytical Methods in Geomechanics, Vol. 13, Issue 1 https://doi.org/10.1002/nag.1610130103	journal	January 1989
Coupling versus uncoupling in soil consolidation Lewis, R. W.; Schrefler, B. A.; Simoni, L. International Journal for Numerical and Analytical Methods in Geomechanics, Vol. 15, Issue 8 https://doi.org/10.1002/nag.1610150803	journal	August 1991
On stability and convergence of finite element approximations of Biot's consolidation problem Murad, Márcio A.; Loula, Abimael F. D. International Journal for Numerical Methods in Engineering, Vol. 37, Issue 4 https://doi.org/10.1002/nme.1620370407	journal	February 1994
Numerical stabilization of Biot's consolidation model by a perturbation on the flow equation Aguilar, G.; Gaspar, F.; Lisbona, F. International Journal for Numerical Methods in Engineering, Vol. 75, Issue 11 https://doi.org/10.1002/nme.2295	journal	September 2008
On convergence of certain finite volume difference discretizations for 1D poroelasticity interface problems Ewing, Richard E.; Iliev, Oleg P.; Lazarov, Raytcho D. Numerical Methods for Partial Differential Equations, Vol. 23, Issue 3 https://doi.org/10.1002/num.20184	journal	January 2007
A coupling of nonconforming and mixed finite element methods for Biot's consolidation model Yi, Son-Young Numerical Methods for Partial Differential Equations, Vol. 29, Issue 5 https://doi.org/10.1002/num.21775	journal	February 2013
Convergence analysis of a new mixed finite element method for Biot's consolidation model Yi, Son-Young Numerical Methods for Partial Differential Equations, Vol. 30, Issue 4 https://doi.org/10.1002/num.21865	journal	February 2014
Diffusion in Poro-Elastic Media Showalter, R. E. Journal of Mathematical Analysis and Applications, Vol. 251, Issue 1 https://doi.org/10.1006/jmaa.2000.7048	journal	November 2000
A stable finite element for the stokes equations Arnold, D. N.; Brezzi, F.; Fortin, M. Calcolo, Vol. 21, Issue 4 https://doi.org/10.1007/BF02576171	journal	December 1984
A coupling of mixed and continuous Galerkin finite element methods for poroelasticity II: the discrete-in-time case Phillips, Phillip Joseph; Wheeler, Mary F. Computational Geosciences, Vol. 11, Issue 2 https://doi.org/10.1007/s10596-007-9044-z	journal	March 2007
A coupling of mixed and continuous Galerkin finite element methods for poroelasticity I: the continuous in time case Phillips, Phillip Joseph; Wheeler, Mary F. Computational Geosciences, Vol. 11, Issue 2 https://doi.org/10.1007/s10596-007-9045-y	journal	March 2007
Overcoming the problem of locking in linear elasticity and poroelasticity: an heuristic approach Phillips, Phillip Joseph; Wheeler, Mary F. Computational Geosciences, Vol. 13, Issue 1 https://doi.org/10.1007/s10596-008-9114-x	journal	December 2008
A $$C^0$$ C 0 -Weak Galerkin Finite Element Method for the Biharmonic Equation Mu, Lin; Wang, Junping; Ye, Xiu Journal of Scientific Computing, Vol. 59, Issue 2 https://doi.org/10.1007/s10915-013-9770-4	journal	August 2013
A Weak Galerkin Finite Element Method for the Maxwell Equations Mu, Lin; Wang, Junping; Ye, Xiu Journal of Scientific Computing, Vol. 65, Issue 1 https://doi.org/10.1007/s10915-014-9964-4	journal	December 2014
A computational study of the weak Galerkin method for second-order elliptic equations Mu, Lin; Wang, Junping; Wang, Yanqiu Numerical Algorithms, Vol. 63, Issue 4 https://doi.org/10.1007/s11075-012-9651-1	journal	October 2012
Improved accuracy in finite element analysis of Biot's consolidation problem Murad, Márcio A.; Loula, Abimael F. D. Computer Methods in Applied Mechanics and Engineering, Vol. 95, Issue 3 https://doi.org/10.1016/0045-7825(92)90193-N	journal	March 1992
A finite difference analysis of Biot's consolidation model Gaspar, F. J.; Lisbona, F. J.; Vabishchevich, P. N. Applied Numerical Mathematics, Vol. 44, Issue 4 https://doi.org/10.1016/S0168-9274(02)00190-3	journal	March 2003
A weak Galerkin finite element method for second-order elliptic problems Wang, Junping; Ye, Xiu Journal of Computational and Applied Mathematics, Vol. 241 https://doi.org/10.1016/j.cam.2012.10.003	journal	March 2013
A modified weak Galerkin finite element method for the Stokes equations Mu, Lin; Wang, Xiaoshen; Ye, Xiu Journal of Computational and Applied Mathematics, Vol. 275 https://doi.org/10.1016/j.cam.2014.08.006	journal	February 2015
A nonconforming finite element method for the Biot’s consolidation model in poroelasticity Hu, Xiaozhe; Rodrigo, Carmen; Gaspar, Francisco J. Journal of Computational and Applied Mathematics, Vol. 310 https://doi.org/10.1016/j.cam.2016.06.003	journal	January 2017
Stability and monotonicity for some discretizations of the Biot’s consolidation model Rodrigo, C.; Gaspar, F. J.; Hu, X. Computer Methods in Applied Mechanics and Engineering, Vol. 298 https://doi.org/10.1016/j.cma.2015.09.019	journal	January 2016
A fully coupled 3-D mixed finite element model of Biot consolidation Ferronato, Massimiliano; Castelletto, Nicola; Gambolati, Giuseppe Journal of Computational Physics, Vol. 229, Issue 12 https://doi.org/10.1016/j.jcp.2010.03.018	journal	June 2010
Weak Galerkin methods for second order elliptic interface problems Mu, Lin; Wang, Junping; Wei, Guowei Journal of Computational Physics, Vol. 250 https://doi.org/10.1016/j.jcp.2013.04.042	journal	October 2013
A stable numerical algorithm for the Brinkman equations by weak Galerkin finite element methods Mu, Lin; Wang, Junping; Ye, Xiu Journal of Computational Physics, Vol. 273 https://doi.org/10.1016/j.jcp.2014.04.017	journal	September 2014
Weak Galerkin finite element methods for Darcy flow: Anisotropy and heterogeneity Lin, Guang; Liu, Jiangguo; Mu, Lin Journal of Computational Physics, Vol. 276 https://doi.org/10.1016/j.jcp.2014.07.001	journal	November 2014
A fully coupled consolidation model of the subsidence of Venice Lewis, R. W.; Schrefler, B. Water Resources Research, Vol. 14, Issue 2 https://doi.org/10.1029/WR014i002p00223	journal	April 1978
General Theory of Three‐Dimensional Consolidation Biot, Maurice A. Journal of Applied Physics, Vol. 12, Issue 2 https://doi.org/10.1063/1.1712886	journal	February 1941
Theory of Elasticity and Consolidation for a Porous Anisotropic Solid Biot, M. A. Journal of Applied Physics, Vol. 26, Issue 2 https://doi.org/10.1063/1.1721956	journal	February 1955
A weak Galerkin mixed finite element method for second order elliptic problems Wang, Junping; Ye, Xiu Mathematics of Computation, Vol. 83, Issue 289 https://doi.org/10.1090/S0025-5718-2014-02852-4	journal	May 2014
Exact Solutions for Two-Dimensional Time-Dependent Flow and Deformation Within a Poroelastic Medium Barry, S. I.; Mercer, G. N. Journal of Applied Mechanics, Vol. 66, Issue 2 https://doi.org/10.1115/1.2791080	journal	June 1999
Asymptotic Behavior of Semidiscrete Finite-Element Approximations of Biot’s Consolidation Problem Murad, Márcio A.; Thomée, Vidar; Loula, Abimael F. D. SIAM Journal on Numerical Analysis, Vol. 33, Issue 3 https://doi.org/10.1137/0733052	journal	June 1996
Stabilized Lowest-Order Finite Element Approximation for Linear Three-Field Poroelasticity Berger, Lorenz; Bordas, Rafel; Kay, David SIAM Journal on Scientific Computing, Vol. 37, Issue 5 https://doi.org/10.1137/15M1009822	journal	January 2015
Consolidation Des Sols (Étude Mathématique) Mandel, J. Géotechnique, Vol. 3, Issue 7 https://doi.org/10.1680/geot.1953.3.7.287	journal	September 1953
The Pore-Pressure Coefficients A and B Skempton, A. W. Géotechnique, Vol. 4, Issue 4 https://doi.org/10.1680/geot.1954.4.4.143	journal	December 1954
Mandel's problem revisited Abousleiman, Y.; Cheng, A. H. -D.; Cui, L. Géotechnique, Vol. 46, Issue 2 https://doi.org/10.1680/geot.1996.46.2.187	journal	June 1996
The existence and uniqueness theorem in Biot's consolidation theory [The existence and uniqueness theorem in Biot's consolidation theory] Ženíšek, Alexander Applications of Mathematics, Vol. 29, Issue 3 https://doi.org/10.21136/AM.1984.104085	journal	January 1984
Finite Difference Schemes for Poro-elastic ProblemS Gaspar, Francisco J.; Lisbona, Francisco J.; Vabishchevich, Petr N. Computational Methods in Applied Mathematics, Vol. 2, Issue 2 https://doi.org/10.2478/cmam-2002-0008	journal	January 2002
A Numerical Study on the Weak Galerkin Method for the Helmholtz Equation Mu, Lin; Wang, Junping; Ye, Xiu Communications in Computational Physics, Vol. 15, Issue 5 https://doi.org/10.4208/cicp.251112.211013a	journal	May 2014

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