doi:10.1515/cmam-2016-0046engMatus, PiotrGaspar Lorenz, Francisco JoséHieu, Le MinhTuyen, Vo Thi KimMonotone difference schemes for weakly coupled elliptic and parabolic systemsART-2017-104080The present paper is devoted to the development of the theory of monotone difference schemes, approximating the so-called weakly coupled system of linear elliptic and quasilinear parabolic equations. Similarly to the scalar case, the canonical form of the vector-difference schemes is introduced and the definition of its monotonicity is given. This definition is closely associated with the property of non-negativity of the solution. Under the fulfillment of the positivity condition of the coefficients, two-side estimates of the approximate solution of these vector-difference equations are established and the important a priori estimate in the uniform norm C is given.2017http://zaguan.unizar.es/record/6527410.1515/cmam-2016-0046http://zaguan.unizar.es/record/65274oai:zaguan.unizar.es:65274info:eu-repo/grantAgreement/EC/H2020/705402/EU/Efficient numerical methods for deformable porous media. Application to carbon dioxide storage./poro sosThis project has received funding from the European Union’s Horizon 2020 research and innovation program under grant agreement No H2020 705402-poro sosComputational Methods in Applied Mathematics 17, 2 (2017), 287-298All rights reservedhttp://www.europeana.eu/rights/rr-f/info:eu-repo/semantics/openAccess