yusuke1997/dblp-id-title huggingface dataset:
The Penalty-Free Nitsche Method and Nonconforming Finite Elements for the Signorini Problem
Mixed Finite Element Approximations of Parabolic Integro-Differential Equations with Nonsmooth Initial Data
An Explicit Construction of Optimal Order Quasi-Monte Carlo Rules for Smooth Integrands
The mpEDMD Algorithm for Data-Driven Computations of Measure-Preserving Dynamical Systems
Discontinuous Galerkin Finite Element Convergence for Incompressible Miscible Displacement Problems of Low Regularity
Multigrid Preconditioning of Linear Systems for Interior Point Methods Applied to a Class of Box-constrained Optimal Control Problems
On the Optimality of Target-Data-Dependent Kernel Greedy Interpolation in Sobolev Reproducing Kernel Hilbert Spaces
Rank-Deficient Nonlinear Least Squares Problems and Subset Selection
Analysis of Complete Radiation Boundary Conditions for Maxwell's Equations
On a Parallel Robin-Type Nonoverlapping Domain Decomposition Method
A Renormalized Newton Method for Liquid Crystal Director Modeling
Gain Coefficients for Scrambled Halton Points
A Compact Difference Scheme for the Biharmonic Equation in Planar Irregular Domains
Compact Alternating Direction Implicit Scheme for the Two-Dimensional Fractional Diffusion-Wave Equation
Wavelet Least Squares Methods for Boundary Value Problems
Elliptic Reconstruction and a Posteriori Error Estimates for Parabolic Problems
Matrix Stabilization Using Differential Equations
A New Discontinuous Finite Volume Method for Elliptic Problems
Flux Recovery and A Posteriori Error Estimators: Conforming Elements for Scalar Elliptic Equations
Order of Convergence of Splitting Schemes for Both Deterministic and Stochastic Nonlinear Schrödinger Equations
Positivity Preserving and Mass Conservative Projection Method for the Poisson-Nernst-Planck Equation
Numerical Approximation of the Best Decay Rate for Some Dissipative Systems
Sensitivity of ODE Solutions and Quantities of Interest with Respect to Component Functions in the Dynamics
Numerical Discretization of Boundary Conditions for First Order Hamilton-Jacobi Equations
Material and Shape Derivative Method for Quasi-Linear Elliptic Systems with Applications in Inverse Electromagnetic Interface Problems
High Order Strong Stability Preserving MultiDerivative Implicit and IMEX Runge-Kutta Methods with Asymptotic Preserving Properties
Fourth-Order Nonoscillatory Upwind and Central Schemes for Hyperbolic Conservation Laws
Local Jacobi Operators and Applications to the p-Version of Finite Element Method in Two Dimensions
A Multipoint Stress Mixed Finite Element Method for Elasticity on Simplicial Grids
Adaptive Solution of Operator Equations Using Wavelet Frames
L p Convergence of the Immersed Boundary Method for Stationary Stokes Problems
Analysis of an SDG Method for the Incompressible Navier-Stokes Equations
Numerical Cubature from Archimedes' Hat-box Theorem
A Collocation Method for the Gurtin-MacCamy Equation with Finite Life-Span
On the Convergence Rate of Randomized Quasi-Monte Carlo for Discontinuous Functions
Numerical Methods and Analysis of Computing Quasiperiodic Systems
Multiple Relaxation Exponential Runge-Kutta Methods for the Nonlinear Schrödinger Equation
Polynomial Interpolation on the Unit Sphere
On a New Class of BDF and IMEX Schemes for Parabolic Type Equations
On the Coefficients in Finite Difference Series Expansions of Derivatives
Analysis of a Semidiscrete Version of the Wigner Equation
Correction to "Strict Diagonal Dominance and Optimal Bounds for the Skeel Condition Number"
Error Analysis of a Dual-parametric Bi-quadratic FEM in Cavitation Computation in Elasticity
Quasi-optimal Error Estimates for Implicit Discretizations of Rate-Independent Evolutions
Convergence of a Second-order Energy-decaying Method for the Viscous Rotating Shallow Water Equation
Interpolation in Lie Groups
On the Convergence of Adaptive Stochastic Collocation for Elliptic Partial Differential Equations with Affine Diffusion
Stochastic Convergence of a Nonconforming Finite Element Method for the Thin Plate Spline Smoother for Observational Data
Effective Discretization of Direct Reconstruction Schemes For Photoacoustic Imaging In Spherical Geometries
A Coupled Prediction Scheme for Solving the Navier-Stokes and Convection-Diffusion Equations
Positivity and Conservation Properties of Some Integration Schemes for Mass Action Kinetics
Divergence-free Scott-Vogelius Elements on Curved Domains
A Unified Analysis for Conforming and Nonconforming Stabilized Finite Element Methods Using Interior Penalty
Optimal Schwarz Waveform Relaxation for the One Dimensional Wave Equation
Mixed Finite Element Methods for the Fully Nonlinear Monge-Ampère Equation Based on the Vanishing Moment Method
Multilevel Higher Order QMC Petrov-Galerkin Discretization for Affine Parametric Operator Equations
Analytic and Gevrey Class Regularity for Parametric Elliptic Eigenvalue Problems and Applications
Counting Via Entropy: New Preasymptotics for the Approximation Numbers of Sobolev Embeddings
A Nonstiff Euler Discretization of the Complex Ginzburg-Landau Equation in One Space Dimension
Adaptive Wavelet Galerkin Methods for Linear Inverse Problems
Strong Stability Preserving Explicit Runge-Kutta Methods of Maximal Effective Order
Preservation of Quadratic Invariants by Semiexplicit Symplectic Integrators for Nonseparable Hamiltonian Systems
Finite Element Discretization Error Analysis of a Surface Tension Force in Two-Phase Incompressible Flows
Finite Element Runge-Kutta Discretizations of Porous Medium-Type Equations
Error Analysis for Time-Fractional Semilinear Parabolic Equations Using Upper and Lower Solutions
Local Error Estimates for SUPG Solutions of Advection-Dominated Elliptic Linear-Quadratic Optimal Control Problems
Convergence of Godunov-Type Schemes for Scalar Conservation Laws under Large Time Steps
Stability and Convergence Analysis of the Extensions of the Kinematically Coupled Scheme for the Fluid-Structure Interaction
Computing Acoustic Waves in an Inhomogeneous Medium of the Plane by a Coupling of Spectral and Finite Elements
Adaptive Spectral Galerkin Methods with Dynamic Marking
Error Estimate of Unconditionally Stable and Decoupled Linear Positivity-Preserving FEM for the Chemotaxis-Stokes Equations
Domain Decomposition for Less Regular Subdomains: Overlapping Schwarz in Two Dimensions
A New Perspective on Kinetic Schemes
Hybrid High-Order and Weak Galerkin Methods for the Biharmonic Problem
Error Estimates for a Finite Element Discretization of a Phase Field Model for Mixtures
Error Analysis of a Semidiscrete Numerical Scheme for Diffusion in Axially Symmetric Surfaces
An Optimal-Order Error Estimate to ELLAM Schemes for Transient Advection-Diffusion Equations on Unstructured Meshes
On the Coupling of the Curved Virtual Element Method with the One-Equation Boundary Element Method for 2D Exterior Helmholtz Problems
An Energy- and Helicity-Conserving Finite Element Scheme for the Navier-Stokes Equations
Sharp Preasymptotic Error Bounds for the Helmholtz \(\boldsymbol{h}\)-FEM
Quasi-optimal Adaptive Pseudostress Approximation of the Stokes Equations
A Bi-Projection Method for Incompressible Bingham Flows with Variable Density, Viscosity, and Yield Stress
Primal Dual Mixed Finite Element Methods for Indefinite Advection-Diffusion Equations
An ODE-Based Method for Computing the Distance of Coprime Polynomials to Common Divisibility
Uniform Convergence of a Linearly Transformed Particle Method for the Vlasov-Poisson System
A New Hydrostatic Reconstruction Scheme Based on Subcell Reconstructions
A Rational Interpolation Scheme with Superpolynomial Rate of Convergence
Multiplier Spaces for the Mortar Finite Element Method in Three Dimensions
Nonlinear Stability Analysis of Area-Preserving Integrators
Pointwise Error Estimates for First-Order div Least-Squares Finite Element Methods and Applications to Superconvergence and A Posteriori Error Estimators
Analysis of Long Time Stability and Errors of Two Partitioned Methods for Uncoupling Evolutionary Groundwater-Surface Water Flows
hp-Discontinuous Galerkin Time-Stepping for Volterra Integrodifferential Equations
Corrigendum: Fourier Spectral Approximation to a Dissipative System Modeling the Flow of Liquid Crystals
How Data Dependent is a Nonlinear Subdivision Scheme? A Case Study Based on Convexity Preserving Subdivision
On Uncertainty Quantification of Eigenvalues and Eigenspaces with Higher Multiplicity
Strong Convergence of a Fully Discrete Finite Element Approximation of the Stochastic Cahn-Hilliard Equation
Inexact Newton-Landweber Iteration in Banach Spaces with NonSmooth Convex Penalty Terms
A Div-Curl Lemma for Edge Elements
Unconditional Stability of Semi-Implicit Discretizations of Singular Flows
The Gauge-Uzawa Finite Element Method. Part I: The Navier-Stokes Equations
Sparse Monte Carlo Method for Nonlocal Diffusion Problems
B-series and Order Conditions for Exponential Integrators
Multigrid Solver for the Inner Problem in Domain Decomposition Methods for p -FEM
Control Volume Approximation of Degenerate Two-Phase Porous Flows
Primal Hybrid Finite Element Method for the Helmholtz Equation
Discontinuous Galerkin Finite Element Approximation of Hamilton-Jacobi-Bellman Equations with Cordes Coefficients
Interpolatory Rational Model Order Reduction of Parametric Problems Lacking Uniform Inf-Sup Stability
On Energy Stable, Maximum-Principle Preserving, Second-Order BDF Scheme with Variable Steps for the Allen-Cahn Equation
Error Analysis of Pressure-Correction Schemes for the Time-Dependent Stokes Equations with Open Boundary Conditions
Krylov Subspace Acceleration of Waveform Relaxation
Two-Sided Bounds for Eigenvalues of Differential Operators with Applications to Friedrichs, Poincaré, Trace, and Similar Constants
On the Strong Convergence of Gradients in Stabilized Degenerate Convex Minimization Problems
An Optimal-Order Numerical Approximation to Variable-order Space-fractional Diffusion Equations on Uniform or Graded Meshes
On the Stability of Evolution Galerkin Schemes Applied to a Two-Dimensional Wave Equation System
Numerical Approximation for a Superreplication Problem under Gamma Constraints
Mesh-Preserving and Energy-Stable Parametric FEM for Geometric Flows of Surfaces
On the Superconvergence of a Hybridizable Discontinuous Galerkin Method for the Cahn-Hilliard Equation
Partially Implicit BDF2 Blends for Convection Dominated Flows
A Randomized Nonmonotone Block Proximal Gradient Method for a Class of Structured Nonlinear Programming
An Engquist-Osher-Type Scheme for Conservation Laws with Discontinuous Flux Adapted to Flux Connections
Attraction Rates, Robustness, and Discretization of Attractors
Asymptotic Error Expansions for the Finite Element Method for Second Order Elliptic Problems in R N , N>=2. I: Local Interior Expansions
Lehmann Bounds and Eigenvalue Error Estimation
Piecewise Divergence-Free Nonconforming Virtual Elements for Stokes Problem in Any Dimensions
A Posteriori Analysis and Adaptive Error Control for Multiscale Operator Decomposition Solution of Elliptic Systems I: Triangular Systems
Convergence Analysis of High Order Algebraic Fractional Step Schemes for Time-Dependent Stokes Equations
A Multipoint Flux Mixed Finite Element Method
Convergence Analysis of the mimetic Finite Difference Method for Elliptic Problems with Staggered Discretizations of Diffusion Coefficients
A Posteriori Error Estimates for Discontinuous Galerkin Time-Stepping Method for Optimal Control Problems Governed by Parabolic Equations
Nonlocal Conservation Laws. A New Class of Monotonicity-Preserving Models
Local Linearization Method for Numerical Integration of Delay Differential Equations
On Convergence of Numerical Solutions for the Compressible MHD System with Exactly Divergence-Free Magnetic Field
An Adaptive Finite Element Method with Perfectly Matched Absorbing Layers for the Wave Scattering by Periodic Structures
Optimal Convergence of the Original DG Method on Special Meshes for Variable Transport Velocity
A Positivity-Preserving Numerical Scheme for a Nonlinear Fourth Order Parabolic System
Methods for Reliable Topology Changes for Perimeter-Regularized Geometric Inverse Problems
Asymptotically Compatible Reproducing Kernel Collocation and Meshfree Integration for Nonlocal Diffusion
A New Regularization Method for the Time Fractional Inverse Advection-Dispersion Problem
Convergence of Time-Stepping Method for Initial and Boundary-Value Frictional Compliant Contact Problems
Characterizing the Stabilization Size for Semi-Implicit Fourier-Spectral Method to Phase Field Equations
Hessian Matrix vs. Gauss-Newton Hessian Matrix
Analysis of a Two-Scale, Locally Conservative Subgrid Upscaling for Elliptic Problems
A Primal-Dual Weak Galerkin Finite Element Method for Fokker-Planck Type Equations
Finite Element Method and its Analysis for a Nonlinear Helmholtz Equation with High Wave Numbers
A Posteriori Modeling Error Estimates for the Assumption of Perfect Incompressibility in the Navier-Stokes Equation
FEM and CIP-FEM for Helmholtz Equation with High Wave Number and Perfectly Matched Layer Truncation
Higher Order QMC Petrov-Galerkin Discretization for Affine Parametric Operator Equations with Random Field Inputs
An Unconstrained Mixed Method for the Biharmonic Problem
Global and Local Pointwise Error Estimates for Finite Element Approximations to the Stokes Problem on Convex Polyhedra
Finite Element Approximation of the Cahn-Hilliard-Cook Equation
Almost Sure and Moment Exponential Stability in the Numerical Simulation of Stochastic Differential Equations
Convergence Analysis of Leapfrog for Geodesics
Convergence Rate of a Schwarz Multilevel Method for the Constrained Minimization of Nonquadratic Functionals
A New Conservative Discontinuous Galerkin Method via Implicit Penalization for the Generalized Korteweg-de Vries Equation
Convergence Analysis of Discrete High-Index Saddle Dynamics
Decoupling of Mixed Methods Based on Generalized Helmholtz Decompositions
Cut Finite Element Method for Divergence-Free Approximation of Incompressible Flow: A Lagrange Multiplier Approach
Anisotropic Mesh Refinement: The Conditioning of Galerkin Boundary Element Matrices and Simple Preconditioners
Strong Stability for Additive Runge-Kutta Methods
On Optimal Convergence Rate of the Rational Krylov Subspace Reduction for Electromagnetic Problems in Unbounded Domains
Decoupled Time Stepping Methods for Fluid-Fluid Interaction
A New Convergence Proof for Finite Volume Schemes Using the Kinetic Formulation of Conservation Laws
Remarks on "On a General Class of Multipoint Root-Finding Methods of High Computational Efficiency"
Full Discretization of Semilinear Stochastic Wave Equations Driven by Multiplicative Noise
Invariant Domains and Second-Order Continuous Finite Element Approximation for Scalar Conservation Equations
A Fast Method for Linear Waves Based on Geometrical Optics
New Time Domain Decomposition Methods for Parabolic Optimal Control Problems I: Dirichlet-Neumann and Neumann-Dirichlet Algorithms
An Efficient Finite Element Method for the Quad-Curl Problem
Optimal Long-Time Decay Rate of Numerical Solutions for Nonlinear Time-Fractional Evolutionary Equations
Superconvergent HDG Methods on Isoparametric Elements for Second-Order Elliptic Problems
L INFINITY - and L 2 -Error Estimates for a Finite Volume Approximation of Linear Advection
Low-Order Discontinuous Petrov-Galerkin Finite Element Methods for Linear Elasticity
Analysis of an Asymptotic Preserving Scheme for the Euler-Poisson System in the Quasineutral Limit
An Analysis of a Broken P 1 -Nonconforming Finite Element Method for Interface Problems
Efficient and Safe Global Constraints for Handling Numerical Constraint Systems
Error Analysis of BDF 1-6 Time-Stepping Methods for the Transient Stokes Problem: Velocity and Pressure Estimates
Ordered Upwind Methods for Static Hamilton-Jacobi Equations: Theory and Algorithms
Optimally Blended Spectral-Finite Element Scheme for Wave Propagation and NonStandard Reduced Integration
Convergence Analysis of the Nonoverlapping Robin-Robin Method for Nonlinear Elliptic Equations
Stable High Order Quadrature Rules for Scattered Data and General Weight Functions
Analysis of Discontinuous Finite Element Methods for Ground Water/Surface Water Coupling
Mesh Independent Superlinear PCG Rates Via Compact-Equivalent Operators
Parametric Raviart-Thomas Elements for Mixed Methods on Domains with Curved Surfaces
Coupling of Finite Elements and Boundary Elements in Electromagnetic Scattering
An Iteration Free Backward Semi-Lagrangian Scheme for Guiding Center Problems
A Posteriori Error Estimates for Finite Element Approximation of Unsteady Incompressible Stochastic Navier-Stokes Equations
High Order Contractive Runge-Kutta Methods for Volterra Functional Differential Equations
Central Differencing Based Numerical Schemes for Hyperbolic Conservation Laws with Relaxation Terms
Preconditioners for Generalized Saddle-Point Problems
A New Lagrange Multiplier Approach for Constructing Structure Preserving Schemes, II. Bound Preserving
Second-Order Accurate TVD Numerical Methods for Nonlocal Nonlinear Conservation Laws
p Interpolation Error Estimates for Edge Finite Elements of Variable Order in Two Dimensions
A Hybrid Collocation Method for Volterra Integral Equations with Weakly Singular Kernels
Uniformly Accurate Nested Picard Iterative Integrators for the Dirac Equation in the Nonrelativistic Limit Regime
On the Convergence of Local Expansions of Layer Potentials
Convergence and Optimality of Adaptive Least Squares Finite Element Methods
Spherical Product Algorithms and the Integration of Smooth Functions with One Singular Point
A Posteriori Error Estimates for Discontinuous Galerkin Methods on Polygonal and Polyhedral Meshes
A Posteriori Error Control for Fully Discrete Crank-Nicolson Schemes
Leapfrog Methods for Relativistic Charged-Particle Dynamics
Asymptotically Compatible Schemes for Stochastic Homogenization
Solving Laplace Problems with Corner Singularities via Rational Functions
Entropy Conservative and Entropy Stable Schemes for Nonconservative Hyperbolic Systems
Approximations of Very Weak Solutions to Boundary-Value Problems
Numerical Analysis of a Unilateral Problem in Planar Thermoelasticity
Computing Multivariate Fekete and Leja Points by Numerical Linear Algebra
The Validity of Johnson-Nédélec's BEM-FEM Coupling on Polygonal Interfaces
Numerical Decomposition of the Solution Sets of Polynomial Systems into Irreducible Components
Least Squares for the Perturbed Stokes Equations and the Reissner-Mindlin Plate
A Trefftz Polynomial Space-Time Discontinuous Galerkin Method for the Second Order Wave Equation
Implicit Runge-Kutta Methods for Lipschitz Continuous Ordinary Differential Equations
Robust Preconditioning and Error Estimates for Optimal Control of the Convection-Diffusion-Reaction Equation with Limited Observation in Isogeometric Analysis
Superconvergence of the Local Discontinuous Galerkin Method for Elliptic Problems on Cartesian Grids
Discontinuous Galerkin Methods for Friedrichs' Systems. Part III. Multifield Theories with Partial Coercivity
Simulation of the Solution of a Viscous Porous Medium Equation by a Particle Method
Multigrid Algorithms for hp-Discontinuous Galerkin Discretizations of Elliptic Problems
Stability Conditions for the Numerical Solution of Convection-Dominated Problems with Skew-Symmetric Discretizations
Error Analysis for a Parabolic PDE Model Problem on a Coupled Moving Domain in a Fully Eulerian Framework
Optimal Biquadratic Finite Volume Element Methods on Quadrilateral Meshes
Variational Mesh Adaptation Methods for Axisymmetrical Problems
A C 1 Virtual Element Method for the Cahn-Hilliard Equation with Polygonal Meshes
A Stability Barrier for Reconstructions from Fourier Samples
Incompressible Finite Elements via Hybridization. Part II: The Stokes System in Three Space Dimensions
Analysis of Constants in Error Estimates for the Finite Element Approximation of Regularized Nonlinear Geometric Evolution Equations
A Spectral Method (of Exponential Convergence) for Singular Solutions of the Diffusion Equation with General Two-Sided Fractional Derivative
Optimal Convergence for Discrete Variational Inequalities Modelling Signorini Contact in 2D and 3D without Additional Assumptions on the Unknown Contact Set
Error Analysis Based on Inverse Modified Differential Equations for Discovery of Dynamics Using Linear Multistep Methods and Deep Learning
Optimal Error Estimates of the Chebyshev-Legendre Spectral Method for Solving the Generalized Burgers Equation
Error Estimates on the Approximate Finite Volume Solution of Convection Diffusion Equations with General Boundary Conditions
On the Long-Time Stability of the Implicit Euler Scheme for the Two-Dimensional Navier-Stokes Equations
POD-ROMs for Incompressible Flows Including Snapshots of the Temporal Derivative of the Full Order Solution
Weighted L 2 -Stability of the Lattice Boltzmann Method
Convergence Analysis of the Monte Carlo Method for the Random Navier-Stokes-Fourier System
High-order Mass- and Energy-conserving SAV-Gauss Collocation Finite Element Methods for the Nonlinear Schrödinger Equation
Local Transparent Boundary Conditions for Wave Propagation in Fractal Trees (II). Error and Complexity Analysis
Wellposedness of Variable-Coefficient Conservative Fractional Elliptic Differential Equations
Two A Posteriori Error Estimates for One-Dimensional Scalar Conservation Laws
Pointwise Gradient Estimate of the Ritz Projection
Piecewise Linear Orthogonal Approximation
Finite Difference Schemes for the "Parabolic" Equation in a Variable Depth Environment with a Rigid Bottom Boundary Condition
Mean Field Games: Convergence of a Finite Difference Method
Fast Multilevel Augmentation Methods for Nonlinear Boundary Integral Equations
Strong Stability Preserving Two-step Runge-Kutta Methods
Asymptotic Preserving Implicit-Explicit Runge-Kutta Methods for Nonlinear Kinetic Equations
CFL Condition and Boundary Conditions for DGM Approximation of Convection-Diffusion
Heuristic Modified Equation Analysis on Oscillations in Numerical Solutions of Conservation Laws
Superconvergence of Discontinuous Galerkin Method for Scalar Nonlinear Hyperbolic Equations
Integral Equation Methods for Elastance and Mobility Problems in Two Dimensions
Godunov-Type Methods for Conservation Laws with a Flux Function Discontinuous in Space
On Optimal Pointwise in Time Error Bounds and Difference Quotients for the Proper Orthogonal Decomposition
Analysis of Schwarz Methods for a Hybridizable Discontinuous Galerkin Discretization
Sharp Uniform Convergence Rate of the Supercell Approximation of a Crystalline Defect
Optimal Importance Sampling Parameter Search for Lévy Processes via Stochastic Approximation
The Discrete Duality Finite Volume Method for Convection-diffusion Problems
Reconstruction of Closely Spaced Small Inclusions
A Multiscale HDG Method for Second Order Elliptic Equations. Part I. Polynomial and Homogenization-Based Multiscale Spaces
A FETI-DP Preconditioner for a Composite Finite Element and Discontinuous Galerkin Method
Multiscale Asymptotic Analysis and Numerical Simulation for the Second Order Helmholtz Equations with Rapidly Oscillating Coefficients Over General Convex Domains
Quantization Based Filtering Method Using First Order Approximation
A New WENO-2r Algorithm with Progressive Order of Accuracy Close to Discontinuities
A New Class of Splitting Methods That Preserve Ergodicity and Exponential Integrability for the Stochastic Langevin Equation
A Mixed Virtual Element Method for Quasi-Newtonian Stokes Flows
Ultra-weak Formulation of a Hypersingular Integral Equation on Polygons and DPG Method with Optimal Test Functions
Postprocessing the Finite Element Method for Semilinear Parabolic Problems
An Algebraic Convergence Theory for Restricted Additive Schwarz Methods Using Weighted Max Norms
Analysis of Energy-Based Blended Quasi-Continuum Approximations
Asymptotic Analysis of Upwind Discontinuous Galerkin Approximation of the Radiative Transport Equation in the Diffusive Limit
Mean-Square Convergence of a Semidiscrete Scheme for Stochastic Maxwell Equations
Numerical Study of Hyperbolic Equations with Integral Constraints Arising in Semiconductor Theory
Comparison Results of Finite Element Methods for the Poisson Model Problem