Mathematics of Computation of the American Mathematical Society, ISSN 0025-5718, 09/2014, Volume 83, Issue 289, pp. 2101 - 2126

A new weak Galerkin (WG) method is introduced and analyzed for the second order elliptic equation formulated as a system of two first order linear equations....

Finite element method | Error rates | Approximation | Polyhedrons | Scalars | Mathematical constants | Polynomials | Vector valued functions | Galerkin methods | Polygons | Mixed finite element methods | Weak galerkin | Finite element methods | Second order elliptic problems | Discrete weak divergence | MATHEMATICS, APPLIED | LAGRANGIAN-MULTIPLIERS | DISCONTINUOUS GALERKIN | MESHES | finite element methods | mixed finite element methods | DIFFERENCE METHOD | discrete weak divergence | second order elliptic problems | DIFFUSION-PROBLEMS | CONVERGENCE | Weak Galerkin

Finite element method | Error rates | Approximation | Polyhedrons | Scalars | Mathematical constants | Polynomials | Vector valued functions | Galerkin methods | Polygons | Mixed finite element methods | Weak galerkin | Finite element methods | Second order elliptic problems | Discrete weak divergence | MATHEMATICS, APPLIED | LAGRANGIAN-MULTIPLIERS | DISCONTINUOUS GALERKIN | MESHES | finite element methods | mixed finite element methods | DIFFERENCE METHOD | discrete weak divergence | second order elliptic problems | DIFFUSION-PROBLEMS | CONVERGENCE | Weak Galerkin

Journal Article

Journal of computational and applied mathematics, ISSN 0377-0427, 2013, Volume 241, Issue 1, pp. 103 - 115

This paper introduces a finite element method by using a weakly defined gradient operator over generalized functions. The use of weak gradients and their...

Mixed finite element methods | Galerkin finite element methods | Second-order elliptic problems | Discrete gradient | MATHEMATICS, APPLIED | LAGRANGIAN-MULTIPLIERS | DISCONTINUOUS GALERKIN | INTERIOR PENALTY | APPROXIMATION | Finite element method | Analysis | Methods | Operators | Approximation | Mathematical analysis | Norms | Mathematical models | Galerkin methods | Optimization

Mixed finite element methods | Galerkin finite element methods | Second-order elliptic problems | Discrete gradient | MATHEMATICS, APPLIED | LAGRANGIAN-MULTIPLIERS | DISCONTINUOUS GALERKIN | INTERIOR PENALTY | APPROXIMATION | Finite element method | Analysis | Methods | Operators | Approximation | Mathematical analysis | Norms | Mathematical models | Galerkin methods | Optimization

Journal Article

International Journal of Numerical Analysis and Modeling, ISSN 1705-5105, 2015, Volume 12, Issue 1, pp. 31 - 53

This paper introduces a new weak Galerkin (WG) finite element method for second order elliptic equations on polytopal meshes. This method, called WG-FEM, is...

Second-order elliptic problems | Finite element methods | Polytopal meshes | Weak Galerkin | Discrete gradient | MATHEMATICS | polytopal meshes | MATHEMATICS, APPLIED | LAGRANGIAN-MULTIPLIERS | discrete gradient | DISCONTINUOUS GALERKIN | finite element methods | second-order elliptic problems | 2ND-ORDER ELLIPTIC PROBLEMS | weak Galerkin

Second-order elliptic problems | Finite element methods | Polytopal meshes | Weak Galerkin | Discrete gradient | MATHEMATICS | polytopal meshes | MATHEMATICS, APPLIED | LAGRANGIAN-MULTIPLIERS | discrete gradient | DISCONTINUOUS GALERKIN | finite element methods | second-order elliptic problems | 2ND-ORDER ELLIPTIC PROBLEMS | weak Galerkin

Journal Article

IEEE Transactions on Signal Processing, ISSN 1053-587X, 06/2017, Volume 65, Issue 12, pp. 3261 - 3276

Source localization based on signal strength measurements has become very popular due to its practical simplicity. However, the severe nonlinearity and...

Uncertainty | Computational modeling | Lagrangian multiplier | Programming | Optimization | Shadow mapping | semidefinite programming (SDP) | block coordinate descent | Source localization | differential received signal strength (DRSS) | least squares | convex optimization | Robustness | Data models | path-loss exponent (PLE) | RSS-BASED LOCATION | SENSOR LOCALIZATION | PARAMETERS | ALGORITHMS | ENGINEERING, ELECTRICAL & ELECTRONIC | Robust statistics | Usage | Computer-generated environments | Computer simulation | Mathematical optimization

Uncertainty | Computational modeling | Lagrangian multiplier | Programming | Optimization | Shadow mapping | semidefinite programming (SDP) | block coordinate descent | Source localization | differential received signal strength (DRSS) | least squares | convex optimization | Robustness | Data models | path-loss exponent (PLE) | RSS-BASED LOCATION | SENSOR LOCALIZATION | PARAMETERS | ALGORITHMS | ENGINEERING, ELECTRICAL & ELECTRONIC | Robust statistics | Usage | Computer-generated environments | Computer simulation | Mathematical optimization

Journal Article

IEEE Transactions on Power Systems, ISSN 0885-8950, 11/2015, Volume 30, Issue 6, pp. 3225 - 3233

This paper introduces a dynamic multiplier-based Lagrangian relaxation approach for the solution to multi-area economic dispatch (MAED) in a fully...

Economics | Sensitivity analysis | Lagrangian multiplier | multi-area economic dispatch (MAED) | Power system dynamics | Lagrangian relaxation | Power generation dispatch | Lagrangian functions | sensitivity analysis | OPTIMAL POWER-FLOW | DC-OPF | IMPLEMENTATION | ENGINEERING, ELECTRICAL & ELECTRONIC | Economic models | Optimization | Exchange | International trade | Multipliers | Algorithms | Dynamics | Mathematical analysis | Mathematical models

Economics | Sensitivity analysis | Lagrangian multiplier | multi-area economic dispatch (MAED) | Power system dynamics | Lagrangian relaxation | Power generation dispatch | Lagrangian functions | sensitivity analysis | OPTIMAL POWER-FLOW | DC-OPF | IMPLEMENTATION | ENGINEERING, ELECTRICAL & ELECTRONIC | Economic models | Optimization | Exchange | International trade | Multipliers | Algorithms | Dynamics | Mathematical analysis | Mathematical models

Journal Article

Applied Energy, ISSN 0306-2619, 03/2017, Volume 190, pp. 949 - 959

•A real-time demand response framework and model is formulated.•Lagrangian relaxation is adopted to decompose the demand response model.•Lagrangian multiplier...

Lagrangian multiplier optimal selection (LMOS) | Sensitivity analysis | Distributed algorithm | Demand response (DR) | Lagrangian relaxation (LR) | RESOURCES | ENERGY | MARKET | SMART GRIDS | ENERGY & FUELS | ALGORITHM | SIDE MANAGEMENT | ENGINEERING, CHEMICAL | Electrical engineering | Case studies | Algorithms | Analysis

Lagrangian multiplier optimal selection (LMOS) | Sensitivity analysis | Distributed algorithm | Demand response (DR) | Lagrangian relaxation (LR) | RESOURCES | ENERGY | MARKET | SMART GRIDS | ENERGY & FUELS | ALGORITHM | SIDE MANAGEMENT | ENGINEERING, CHEMICAL | Electrical engineering | Case studies | Algorithms | Analysis

Journal Article

Mathematics of Computation of the American Mathematical Society, ISSN 0025-5718, 03/2018, Volume 87, Issue 310, pp. 515 - 545

primal-dual weak Galerkin finite element method. Error estimates of optimal order are derived for the corresponding finite element approximations in a discrete...

Cord`es condition | Polyhedral meshes | Weak Hessian operator | Discontinuous coefficients | Finite element methods | Weak Galerkin | Non-divergence form | MATHEMATICS, APPLIED | LAGRANGIAN-MULTIPLIERS | polyhedral meshes | APPROXIMATION | finite element methods | discontinuous coefficients | CORDES COEFFICIENTS | BIHARMONIC EQUATION | non-divergence form | weak Hessian operator | Cordes condition

Cord`es condition | Polyhedral meshes | Weak Hessian operator | Discontinuous coefficients | Finite element methods | Weak Galerkin | Non-divergence form | MATHEMATICS, APPLIED | LAGRANGIAN-MULTIPLIERS | polyhedral meshes | APPROXIMATION | finite element methods | discontinuous coefficients | CORDES COEFFICIENTS | BIHARMONIC EQUATION | non-divergence form | weak Hessian operator | Cordes condition

Journal Article

SIAM Journal on Numerical Analysis, ISSN 0036-1429, 2016, Volume 54, Issue 6, pp. 3332 - 3356

We develop two families of mixed finite elements on quadrilateral meshes for approximating (u,p) solving a second order elliptic equation in mixed form....

Reduced H(div)-approximation | Divergence approximation | Inf-sup stable | Second order elliptic equation | Full H(div)-approximation | Mixed methods | second order elliptic equation | MATHEMATICS, APPLIED | LAGRANGIAN-MULTIPLIERS | SOBOLEV SPACES | MESHES | mixed methods | APPROXIMATION | inf-sup stable | divergence approximation | reduced H(div)-approximation | full H(div)-approximation

Reduced H(div)-approximation | Divergence approximation | Inf-sup stable | Second order elliptic equation | Full H(div)-approximation | Mixed methods | second order elliptic equation | MATHEMATICS, APPLIED | LAGRANGIAN-MULTIPLIERS | SOBOLEV SPACES | MESHES | mixed methods | APPROXIMATION | inf-sup stable | divergence approximation | reduced H(div)-approximation | full H(div)-approximation

Journal Article

9.
Full Text
Preconditioners for saddle point systems with trace constraints coupling 2d and 1d domains

SIAM Journal on Scientific Computing, ISSN 1064-8275, 2016, Volume 38, Issue 6, pp. B962 - B987

We study preconditioners for a model problem describing the coupling of two elliptic subproblems posed over domains with different topological dimension by a...

Lagrange multipliers | Preconditioning | Saddle-point problem | MATRIX | MATHEMATICS, APPLIED | LAGRANGIAN-MULTIPLIERS | saddle-point problem | APPROXIMATION | SPACES | PERFORMANCE | NORMS | EQUATIONS | FINITE-ELEMENT-METHOD | preconditioning

Lagrange multipliers | Preconditioning | Saddle-point problem | MATRIX | MATHEMATICS, APPLIED | LAGRANGIAN-MULTIPLIERS | saddle-point problem | APPROXIMATION | SPACES | PERFORMANCE | NORMS | EQUATIONS | FINITE-ELEMENT-METHOD | preconditioning

Journal Article

Computers and Mathematics with Applications, ISSN 0898-1221, 11/2017, Volume 74, Issue 9, pp. 2047 - 2055

In this paper we discuss mixed finite element methods for nearly incompressible elasticity. We show that if a method uses the hydrostatic pressure as unknown,...

Stability conditions | Mixed finite element methods | Incompressible elasticity | MATHEMATICS, APPLIED | LAGRANGIAN-MULTIPLIERS | EQUATIONS | FLOW

Stability conditions | Mixed finite element methods | Incompressible elasticity | MATHEMATICS, APPLIED | LAGRANGIAN-MULTIPLIERS | EQUATIONS | FLOW

Journal Article

Journal of Computational Physics, ISSN 0021-9991, 09/2014, Volume 273, pp. 327 - 342

This paper presents a stable numerical algorithm for the Brinkman equations by using weak Galerkin (WG) finite element methods. The Brinkman equations can be...

Weak Galerkin | Finite element methods | The Brinkman equations | Polyhedral meshes | LAGRANGIAN-MULTIPLIERS | COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS | FLOWS | PHYSICS, MATHEMATICAL | STOKES | Finite element method | Algorithms | Permeability | Analysis | Methods | Numerical analysis | Computational fluid dynamics | Computer simulation | Mathematical analysis | Fluid flow | Mathematical models | Stokes law (fluid mechanics) | Mathematics - Numerical Analysis

Weak Galerkin | Finite element methods | The Brinkman equations | Polyhedral meshes | LAGRANGIAN-MULTIPLIERS | COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS | FLOWS | PHYSICS, MATHEMATICAL | STOKES | Finite element method | Algorithms | Permeability | Analysis | Methods | Numerical analysis | Computational fluid dynamics | Computer simulation | Mathematical analysis | Fluid flow | Mathematical models | Stokes law (fluid mechanics) | Mathematics - Numerical Analysis

Journal Article

Computer Methods in Applied Mechanics and Engineering, ISSN 0045-7825, 10/2016, Volume 310, pp. 475 - 494

A variety of numerical approximation schemes for boundary value problems suffer from so-called locking-phenomena. It is well known that in such cases several...

Lagrange-multiplier | SKA-element | Anisotropic hyperelasticity | Mixed finite elements | EXISTENCE | LAGRANGIAN-MULTIPLIERS | APPROXIMATIONS | CONSTITUTIVE EQUATIONS | HYPERELASTICITY | INCOMPATIBLE MODES | FORMULATION | NONLINEAR ELASTICITY | MATHEMATICS, INTERDISCIPLINARY APPLICATIONS | MECHANICS | ENGINEERING, MULTIDISCIPLINARY | FRAMEWORK | GENERATION | Anisotropy | Kinematics

Lagrange-multiplier | SKA-element | Anisotropic hyperelasticity | Mixed finite elements | EXISTENCE | LAGRANGIAN-MULTIPLIERS | APPROXIMATIONS | CONSTITUTIVE EQUATIONS | HYPERELASTICITY | INCOMPATIBLE MODES | FORMULATION | NONLINEAR ELASTICITY | MATHEMATICS, INTERDISCIPLINARY APPLICATIONS | MECHANICS | ENGINEERING, MULTIDISCIPLINARY | FRAMEWORK | GENERATION | Anisotropy | Kinematics

Journal Article

Journal of computational and applied mathematics, ISSN 0377-0427, 2018, Volume 341, pp. 127 - 143

This paper introduces new discretization schemes for time-harmonic Maxwell equations in a connected domain by using the weak Galerkin (WG) finite element...

Time-harmonic | Polygonal/polyhedral meshes | Weak curl | Weak Galerkin | Finite element methods | Maxwell equations | Weak divergence | MATHEMATICS, APPLIED | LAGRANGIAN-MULTIPLIERS | APPROXIMATION | 2ND-ORDER ELLIPTIC PROBLEMS | BIHARMONIC EQUATION | Finite element method | Analysis | Methods

Time-harmonic | Polygonal/polyhedral meshes | Weak curl | Weak Galerkin | Finite element methods | Maxwell equations | Weak divergence | MATHEMATICS, APPLIED | LAGRANGIAN-MULTIPLIERS | APPROXIMATION | 2ND-ORDER ELLIPTIC PROBLEMS | BIHARMONIC EQUATION | Finite element method | Analysis | Methods

Journal Article

Computers and Mathematics with Applications, ISSN 0898-1221, 04/2017, Volume 73, Issue 8, pp. 1684 - 1696

This work concerns finite element analysis of the evolutionary Stokes equation with inhomogeneous Dirichlet boundary data. The Dirichlet boundary data are...

Inhomogeneous Dirichlet boundary data | Error estimates | Lagrange multipliers | Evolutionary Stokes equations | Finite element approximations | MATHEMATICS, APPLIED | LAGRANGIAN-MULTIPLIERS | FINITE-ELEMENT APPROXIMATION

Inhomogeneous Dirichlet boundary data | Error estimates | Lagrange multipliers | Evolutionary Stokes equations | Finite element approximations | MATHEMATICS, APPLIED | LAGRANGIAN-MULTIPLIERS | FINITE-ELEMENT APPROXIMATION

Journal Article

International Journal for Numerical Methods in Engineering, ISSN 0029-5981, 04/2016, Volume 106, Issue 4, pp. 278 - 297

Summary A stabilized scheme is developed for mixed finite element methods for strongly coupled diffusion problems in solids capable of large deformations....

coupled diffusion | inf‐sup condition | hourglass instabilities | finite element analysis | enhanced assumed strain | Enhanced assumed strain | Finite element analysis | Hourglass instabilities | Coupled diffusion | Inf-sup condition | LAGRANGIAN-MULTIPLIERS | STABILITY | STRAIN METHODS | inf-sup condition | INCOMPATIBLE MODES | FORMULATION | CONSTRAINT | NONLINEAR ELASTICITY | HOMOGENIZATION | PRINCIPLES | MATHEMATICS, INTERDISCIPLINARY APPLICATIONS | ENGINEERING, MULTIDISCIPLINARY | STABILIZATION TECHNIQUE | Finite element method | Methods | Stability | Mathematical analysis | Cures | Instability | Mathematical models | Diffusion | Strain

coupled diffusion | inf‐sup condition | hourglass instabilities | finite element analysis | enhanced assumed strain | Enhanced assumed strain | Finite element analysis | Hourglass instabilities | Coupled diffusion | Inf-sup condition | LAGRANGIAN-MULTIPLIERS | STABILITY | STRAIN METHODS | inf-sup condition | INCOMPATIBLE MODES | FORMULATION | CONSTRAINT | NONLINEAR ELASTICITY | HOMOGENIZATION | PRINCIPLES | MATHEMATICS, INTERDISCIPLINARY APPLICATIONS | ENGINEERING, MULTIDISCIPLINARY | STABILIZATION TECHNIQUE | Finite element method | Methods | Stability | Mathematical analysis | Cures | Instability | Mathematical models | Diffusion | Strain

Journal Article

SIAM journal on numerical analysis, ISSN 1095-7170, 2017, Volume 55, Issue 6, pp. 2718 - 2744

We discretize the Lagrange multiplier formulation of the obstacle problem by mixed and stabilized finite element methods. A priori and a posteriori error...

Stabilized finite elements | Mixed finite elements | Obstacle problem | MATHEMATICS, APPLIED | LAGRANGIAN-MULTIPLIERS | obstacle problem | SADDLE-POINT PROBLEMS | APPROXIMATION | BOUNDARY-CONDITIONS | VARIATIONAL-INEQUALITIES | NUMERICAL-SOLUTION | POSTERIORI ERROR ESTIMATORS | CONTACT PROBLEMS | STOKES PROBLEM | mixed finite elements | COMPUTATIONAL FLUID-DYNAMICS | stabilized finite elements | Mathematics - Numerical Analysis

Stabilized finite elements | Mixed finite elements | Obstacle problem | MATHEMATICS, APPLIED | LAGRANGIAN-MULTIPLIERS | obstacle problem | SADDLE-POINT PROBLEMS | APPROXIMATION | BOUNDARY-CONDITIONS | VARIATIONAL-INEQUALITIES | NUMERICAL-SOLUTION | POSTERIORI ERROR ESTIMATORS | CONTACT PROBLEMS | STOKES PROBLEM | mixed finite elements | COMPUTATIONAL FLUID-DYNAMICS | stabilized finite elements | Mathematics - Numerical Analysis

Journal Article

Yugoslav Journal of Operations Research, ISSN 0354-0243, 2015, Volume 25, Issue 3, pp. 387 - 395

In this paper the notion of Strict Benson proper-ε-efficient solution for a vector optimization problem with set-valued maps is introduced. The scalarization...

Ic-cone-convexlikeness | Scalarization | Lagrangian Multipliers | Set-valued Maps | Strict Benson proper-ε-efficiency | scalarization | ε-Lagrangian Multipliers

Ic-cone-convexlikeness | Scalarization | Lagrangian Multipliers | Set-valued Maps | Strict Benson proper-ε-efficiency | scalarization | ε-Lagrangian Multipliers

Journal Article

Computer Methods in Applied Mechanics and Engineering, ISSN 0045-7825, 01/2019, Volume 343, pp. 297 - 313

We approximate the spectra of a class of 2n-order differential operators using isogeometric analysis in mixed formulations. This class includes a wide range of...

Isogeometric analysis | Finite elements | Eigenvalue problem | Differential operators | Spectral approximation | Quadratures | LAGRANGIAN-MULTIPLIERS | ENERGY | FINITE-ELEMENT METHODS | MATHEMATICS, INTERDISCIPLINARY APPLICATIONS | MECHANICS | NAVIER-STOKES EQUATIONS | SPLINE SPACES | ENGINEERING, MULTIDISCIPLINARY | INTEGRATION | FLUCTUATIONS | QUADRATURE-RULES | GALERKIN | ERROR | Mines and mineral resources | Analysis

Isogeometric analysis | Finite elements | Eigenvalue problem | Differential operators | Spectral approximation | Quadratures | LAGRANGIAN-MULTIPLIERS | ENERGY | FINITE-ELEMENT METHODS | MATHEMATICS, INTERDISCIPLINARY APPLICATIONS | MECHANICS | NAVIER-STOKES EQUATIONS | SPLINE SPACES | ENGINEERING, MULTIDISCIPLINARY | INTEGRATION | FLUCTUATIONS | QUADRATURE-RULES | GALERKIN | ERROR | Mines and mineral resources | Analysis

Journal Article

Computer Methods in Applied Mechanics and Engineering, ISSN 0045-7825, 08/2017, Volume 322, pp. 137 - 166

For materials that display viscoelastic behavior, adequate description of their failure requires accurate prediction of damage initiation, propagation and...

Viscoelasticity | Damage mechanics | Gradient damage | Prony series | Mesh independence | Damage regularization | LAGRANGIAN-MULTIPLIERS | ENHANCED DAMAGE | CONSTITUTIVE MODEL | GROWING DAMAGE | ASPHALT CONCRETE | FRACTURE | MATHEMATICS, INTERDISCIPLINARY APPLICATIONS | MECHANICS | PARTICULATE COMPOSITES | ENGINEERING, MULTIDISCIPLINARY | QUASI-BRITTLE MATERIALS | NONLOCAL ELASTICITY | CONTINUUM | Thermodynamics | Analysis

Viscoelasticity | Damage mechanics | Gradient damage | Prony series | Mesh independence | Damage regularization | LAGRANGIAN-MULTIPLIERS | ENHANCED DAMAGE | CONSTITUTIVE MODEL | GROWING DAMAGE | ASPHALT CONCRETE | FRACTURE | MATHEMATICS, INTERDISCIPLINARY APPLICATIONS | MECHANICS | PARTICULATE COMPOSITES | ENGINEERING, MULTIDISCIPLINARY | QUASI-BRITTLE MATERIALS | NONLOCAL ELASTICITY | CONTINUUM | Thermodynamics | Analysis

Journal Article

Computer Methods in Applied Mechanics and Engineering, ISSN 0045-7825, 08/2015, Volume 293, pp. 348 - 374

A displacement-based Galerkin meshfree method for large deformation analysis of nearly-incompressible elastic solids is presented. Nodal discretization of the...

Delaunay meshes | Meshfree methods | Maximum-entropy approximation | [formula omitted]-bar method | Large deformations | Hyperelasticity | F-bar method | CONFORMING NODAL INTEGRATION | LAGRANGIAN-MULTIPLIERS | APPROXIMATION | ELASTICITY | LINEAR TRIANGLES | MATHEMATICS, INTERDISCIPLINARY APPLICATIONS | MECHANICS | ENGINEERING, MULTIDISCIPLINARY | TETRAHEDRAL ELEMENT | SOLIDS | NUMERICAL-INTEGRATION | FINITE-ELEMENT FORMULATION | FREE GALERKIN METHOD | Mechanical engineering | Analysis | Green technology

Delaunay meshes | Meshfree methods | Maximum-entropy approximation | [formula omitted]-bar method | Large deformations | Hyperelasticity | F-bar method | CONFORMING NODAL INTEGRATION | LAGRANGIAN-MULTIPLIERS | APPROXIMATION | ELASTICITY | LINEAR TRIANGLES | MATHEMATICS, INTERDISCIPLINARY APPLICATIONS | MECHANICS | ENGINEERING, MULTIDISCIPLINARY | TETRAHEDRAL ELEMENT | SOLIDS | NUMERICAL-INTEGRATION | FINITE-ELEMENT FORMULATION | FREE GALERKIN METHOD | Mechanical engineering | Analysis | Green technology

Journal Article

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