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: "enforcing the non negativity constraint and maximum principles for diffusion with decay on general computational grids"
  Abstract: In this paper, we consider anisotropic diffusion with decay, which takes the form �(x)c(x) div(D(x)grad(c(x))) = f(x) with decay coefficient�(x) � 0, and diffusivity coefficient D(x) to be a second-order symmetric and positive definite tensor. It is well-known that this partic- ular equation is a second-order elliptic equation, and satisfies a maximum principle under certain regularity assumptions. However, the finite element implementation of the classical Galerkin for- mulation for both anisotropic and isotropic diffusion with decay does not respect the maximum principle. Put differently, the classical Galerkin formulation violates the discrete maximum princi- ple for diffusion with decay even on structured computational meshes. We first show that the numerical accuracy of the classical Galerkin formulation deteriorates dramatically with an increase infor isotropic media and violates the discrete maximum prin- ciple. However, in the case of isotropic media, the extent of violation decreases with the mesh refinement. We then show that, in the case of anisotropic media, the classical Galerkin formulation for anisotropic diffusion with decay violates the discrete maximum principle even at lower values of decay coefficient and does not vanish with mesh refinement. We then present a methodology for enforcing maximum principles under the classical Galerkin formulation for anisotropic diffusion with decay on general computational grids using optimization techniques. Representative numer- ical results (which take into account anisotropy and heterogeneity) are presented to illustrate the performance of the proposed formulation. In this paper we consider heterogeneous anisotropic diffusion with decay, which takes the form: �(x)c(x)−div(D(x)grad(c(x))) = f(x) with �(x) � 0 and D(x) is a symmetric and positive definite second-order tensor. This equation is a linear second-order elliptic partial differential equation (21). There are many important problems in Mathematical Physics which give rise to this equation (60). Also, this equation arises in numerical methods and mathematical analysis of transient problems (35). Some of these cases include:

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 "modeling flow in porous media with double porosity permeability a stabilized mixed formulation error analysis and numerical solutions"):
  with members:
    - "mechanics based solution verification for porous media models"
    - "dolfin automated finite element computing"
    - "on the stability of bubble functions and a stabilized mixed finite element formulation for the stokes problem"
    - "a numerical study of fluids with pressure dependent viscosity flowing through a rigid porous medium"

Connected through hyperedge HE-3 (induced by source paper "balson bayesian least squares optimization with nonnegative l1 norm constraint"):
  with members:
    - "comparing measures of sparsity"

Connected through hyperedge HE-4 (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-5 (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"
    - "non negative mixed finite element formulations for a tensorial diffusion equation"
    - "mesh algorithms for pde with sieve i mesh distribution"

Connected through hyperedge HE-6 (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"
    - "well centered triangulation"
    - "non negative mixed finite element formulations for a tensorial diffusion equation"

Connected through hyperedge HE-7 (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"
    - "on the performance of high order finite elements with respect to maximum principles and the non negative constraint for diffusion type equations"
    - "non negative mixed finite element formulations for a tensorial diffusion equation"

Connected through hyperedge HE-8 (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"
    - "on dual schur domain decomposition method for linear first order transient problems"
    - "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)