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: "non negative mixed finite element formulations for a tensorial diffusion equation"
  Abstract: We consider the tensorial diffusion equation, and address the discrete maximum-minimum principle of mixed finite element formulations. In particular, we address non-negative solutions (which is a special case of the maximum-minimum principle) of mixed finite element formulations. It is well-known that the classical finite element formulations (like the single-field Galerkin formulation, and Raviart-Thomas, variational multiscale, and Galerkin/least-squares mixed formulations) do not produce non-negative solutions (that is, they do not satisfy the discrete maximum-minimum principle) on arbitrary meshes and for strongly anisotropic diffusivity coefficients. In this paper, we present two non-negative mixed finite element formulations for tensorial diffusion equations based on constrained optimization techniques. These proposed mixed formulations produce non-negative numerical solutions on arbitrary meshes for low-order (i.e., linear, bilinear and trilinear) finite elements. The first formulation is based on the Raviart-Thomas spaces, and the second non-negative formulation is based on the variational multiscale formulation. For the former formulation we comment on the effect of adding the non-negative constraint on the local mass balance property of the Raviart-Thomas formulation. We perform numerical convergence analysis of the proposed optimization-based non-negative mixed formulations. We also study the performance of the active set strategy for solving the resulting constrained optimization problems. The overall performance of the proposed formulation is illustrated on three canonical test problems.

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 "variational inequality approach to enforcing the non negative constraint for advection diffusion equations"):
  with members:
    - "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"
    - "a parallel edge orientation algorithm for quadrilateral meshes"
    - "a structure exploiting numbering algorithm for finite elements on extruded meshes and its performance evaluation in firedrake"
    - "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-3 (induced by source paper "large scale optimization based non negative computational framework for diffusion equations parallel implementation and performance studies"):
  with members:
    - "flexible scalable mesh and data management using petsc dmplex"
    - "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"
    - "achieving high performance with unified residual evaluation"
    - "a numerical methodology for enforcing maximum principles and the non negative constraint for transient diffusion equations"
    - "enforcing the non negativity constraint and maximum principles for diffusion with decay on general computational grids"
    - "mesh algorithms for pde with sieve i mesh distribution"

Connected through hyperedge HE-4 (induced by source paper "do current lattice boltzmann methods for diffusion and advection diffusion equations respect maximum principle and the non negative constraint"):
  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"

Connected through hyperedge HE-5 (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 mixed formulation for a modification to darcy equation based on picard linearization and numerical solutions to large scale realistic problems"
    - "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"

Connected through hyperedge HE-6 (induced by source paper "a numerical framework for diffusion controlled bimolecular reactive systems to enforce maximum principles and the non negative constraint"):
  with members:
    - "a numerical methodology for enforcing maximum principles and the non negative constraint for transient diffusion equations"
    - "enforcing the non negativity constraint and maximum principles for diffusion with decay on general computational grids"
    - "on the performance of high order finite elements with respect to maximum principles and the non negative constraint for diffusion type equations"

Connected through hyperedge HE-7 (induced by source paper "a numerical methodology for enforcing maximum principles and the non negative constraint for transient diffusion equations"):
  with members:
    - "a numerical framework for diffusion controlled bimolecular reactive systems to enforce maximum principles and the non negative constraint"
    - "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"
    - "on dual schur domain decomposition method for linear first order transient problems"

Connected through hyperedge HE-8 (induced by source paper "a framework for coupled deformation diffusion analysis with application to degradation healing"):
  with members:
    - "enforcing the non negativity constraint and maximum principles for diffusion with decay on general computational grids"
    - "well centered triangulation"

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)