human: Given a node-centered hypergraph: <hypergraph>, where nodes represent papers and hyperedges represent sets of papers co-cited by a source paper.

Details of the hypergraph:
Center node: "a mixed formulation for a modification to darcy equation based on picard linearization and numerical solutions to large scale realistic problems"
  Abstract: In this paper we consider a modification to Darcy equation by taking into account the dependence of viscosity on the pressure. We present a stabilized mixed formulation for the resulting governing equations. Equal-order interpolation for the velocity and pressure is considered, and shown to be stable (which is not the case under the classical mixed formulation). The proposed mixed formulation is tested using a wide variety of numerical examples. The proposed formulation is also implemented in a parallel setting, and the performance of the formulation for large-scale problems is illustrated using a representative problem. Two practical and technologically important problems, one each on enhanced oil recovery and geological carbon-dioxide sequestration, are solved using the proposed formulation. The numerical examples show that the predictions based on Darcy model are qualitatively and quantitatively different from that of the predictions based on the modified Darcy model, which takes into account the dependence of the viscosity on the pressure. In particular, the numerical example on the geological carbon-dioxide sequestration shows that Darcy model over-predicts the leakage into an abandoned well when compared to that of the modified Darcy model. On the other hand, the modified Darcy model predicts higher pressures and higher pressure gradients near the injection well. These predictions have dire consequences in predicting damage and fracture zones, and designing the seal, whose integrity is crucial to the safety of a geological carbon-dioxide sequestration geosystem.

Connected through hyperedge HE-1 (induced by source paper "a scalable variational inequality approach for flow through porous media models with pressure dependent viscosity"):
  with members:
    - "a performance spectrum for parallel computational frameworks that solve pdes"
    - "firedrake automating the finite element method by composing abstractions"
    - "large scale optimization based non negative computational framework for diffusion equations parallel implementation and performance studies"
    - "an algorithm for the optimization of finite element integration loops"
    - "variational inequality approach to enforcing the non negative constraint for advection diffusion equations"
    - "cross loop optimization of arithmetic intensity for finite element local assembly"
    - "on mesh restrictions to satisfy comparison principles maximum principles and the non negative constraint recent developments and new results"
    - "a numerical framework for diffusion controlled bimolecular reactive systems to enforce maximum principles and the non negative constraint"

Connected through hyperedge HE-2 (induced by source paper "on mesh restrictions to satisfy comparison principles maximum principles and the non negative constraint recent developments and new results"):
  with members:
    - "a numerical framework for diffusion controlled bimolecular reactive systems to enforce maximum principles and the non negative constraint"
    - "a numerical methodology for enforcing maximum principles and the non negative constraint for transient diffusion equations"
    - "a framework for coupled deformation diffusion analysis with application to degradation healing"
    - "enforcing the non negativity constraint and maximum principles for diffusion with decay on general computational grids"
    - "well centered triangulation"
    - "non negative mixed finite element formulations for a tensorial diffusion equation"

Question: Please tell me which class the center node belongs to. The 40 classes are: cs.NA(Numerical Analysis), cs.MM(Multimedia), cs.LO(Logic in Computer Science), cs.CY(Computers and Society), cs.CR(Cryptography and Security), cs.DC(Distributed, Parallel, and Cluster Computing), cs.HC(Human-Computer Interaction), cs.CE(Computational Engineering, Finance, and Science), cs.NI(Networking and Internet Architecture), cs.CC(Computational Complexity), cs.AI(Artificial Intelligence), cs.MA(Multiagent Systems), cs.GL(General Literature), cs.NE(Neural and Evolutionary Computing), cs.SC(Symbolic Computation), cs.AR(Hardware Architecture), cs.CV(Computer Vision and Pattern Recognition), cs.GR(Graphics), cs.ET(Emerging Technologies), cs.SY(Systems and Control), cs.CG(Computational Geometry), cs.OH(Other Computer Science), cs.PL(Programming Languages), cs.SE(Software Engineering), cs.LG(Machine Learning), cs.SD(Sound), cs.SI(Social and Information Networks), cs.RO(Robotics), cs.IT(Information Theory), cs.PF(Performance), cs.CL(Computation and Language), cs.IR(Information Retrieval), cs.MS(Mathematical Software), cs.FL(Formal Languages and Automata Theory), cs.DS(Data Structures and Algorithms), cs.OS(Operating Systems), cs.GT(Computer Science and Game Theory), cs.DB(Databases), cs.DL(Digital Libraries), cs.DM(Discrete Mathematics). Directly output the class name.

gpt: cs.NA(Numerical Analysis)