scientific article; zbMATH DE number 635667

zbMath0803.65088MaRDI QIDQ4303980

Alberto Valli, Alfio M. Quarteroni

Publication date: 8 September 1994

Title: zbMATH Open Web Interface contents unavailable due to conflicting licenses.

zbMATH Keywords

algorithmsNavier-Stokes equationsfinite element methoddomain decompositionpreconditioningconvection-diffusion problemsfinite volume methodsnonlinearmultigridlinearfinite differencespectral methodhyperbolic equationsdirect and iterative solvers

Mathematics Subject Classification ID

Numerical computation of solutions to systems of equations (65H10) Navier-Stokes equations (35Q30) Research exposition (monographs, survey articles) pertaining to numerical analysis (65-02) Numerical linear algebra (65Fxx) Numerical methods for partial differential equations, initial value and time-dependent initial-boundary value problems (65Mxx) Numerical methods for partial differential equations, boundary value problems (65Nxx) Parabolic equations and parabolic systems (35Kxx) Hyperbolic equations and hyperbolic systems (35Lxx) Elliptic equations and elliptic systems (35Jxx)

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incompressible viscous flow in an expansion channel, Analysis of two-level domain decomposition preconditioners based on aggregation, A posteriorierror bounds for reduced-basis approximations of parametrized parabolic partial differential equations, NUMERICAL APPROXIMATION OF CONTROLLABILITY OF TRAJECTORIES FOR EULER–BERNOULLI THERMOELASTIC PLATES, A PARALLEL SOLVER FOR REACTION–DIFFUSION SYSTEMS IN COMPUTATIONAL ELECTROCARDIOLOGY, Advanced Implicit Meshless Approaches for the Rayleigh–Stokes Problem for a Heated Generalized Second Grade Fluid with Fractional Derivative, An Enriched Edge-Based Smoothed FEM for Linear Elastic Fracture Problems, Modeling the cardiac electromechanical function: A mathematical journey, Finite point method of nonlinear convection diffusion equation, On the Coupling of the Curved Virtual Element Method with the One-Equation Boundary Element Method for 2D Exterior Helmholtz Problems, Density function of numerical solution of splitting AVF scheme for stochastic Langevin equation, A theoretical study of COmpRessed SolvING for advection-diffusion-reaction problems, Efficient reduced-basis treatment of nonaffine and nonlinear partial differential equations, Space-time finite element methods stabilized using bubble function spaces, BDDC Algorithms with deluxe scaling and adaptive selection of primal constraints for Raviart-Thomas vector fields, Analysis of dynamic ruptures generating seismic waves in a self-gravitating planet: An iterative coupling scheme and well-posedness, Understanding Mass Transfer Directions via Data-Driven Models with Application to Mobile Phone Data, INTERNODES for Heterogeneous Couplings, INTERNODES for Elliptic Problems, Sixth-Order Adaptive Non-uniform Grids for Singularly Perturbed Boundary Value Problems, A Reduced Basis Method for Coercive Equations with an Exact Solution Certificate and Spatio-Parameter Adaptivity: Energy-Norm and Output Error Bounds, Stabilized Weighted Reduced Basis Methods for Parametrized Advection Dominated Problems with Random Inputs, Application of direct extended modified algebraic method of Bogoyavlenskii equation on lower and upper bounds in managing and optimizing queues, Simulations of autonomous fluid pulses between active elastic walls using the 1D-IRBFN method, Numerical simulations for the dynamics of flexural shells, A mixed virtual element method for the Navier–Stokes equations, Analysis of an augmented fully-mixed formulation for the coupling of the Stokes and heat equations, A Sparse Grid Stochastic Collocation Discontinuous Galerkin Method for Constrained Optimal Control Problem Governed by Random Convection Dominated Diffusion Equations, A variational subgrid scale model for transient incompressible flows, Computational electrocardiology: mathematical and numerical modeling, Exponential Quadrature Rules Without Order Reduction for Integrating Linear Initial Boundary Value Problems, Inverse Monotonicity of Elliptic Operators in Variational Form, Hermite Type Spline Spaces over Rectangular Meshes with Complex Topological Structures, Efficient Time-Stepping/Spectral Methods for the Navier-Stokes-Nernst-Planck-Poisson Equations, Error estimates for finite element approximations of parabolic equations with measure data, The Generalized Arrow-Hurwicz Method with Applications to Fluid Computation, Full Discretization Scheme for the Dynamics of Elliptic Membrane Shell Model, Algebraic Multigrid Block Preconditioning for Multi-Group Radiation Diffusion Equations, Analysis of augmented three-field macro-hybrid mixed finite element schemes, Unnamed Item, A locally conservative LDG method for the incompressible Navier-Stokes equations, A numerical method for spatial diffusion in age-structured populations, Analysis of an Euler implicit-mixed finite element scheme for reactive solute transport in porous media, HP-finite element approximations on non-matching grids for partial differential equations with non-negative characteristic form, Multiscale Finite Element Methods for Advection-Dominated Problems in Perforated Domains, A domain splitting method for heat conduction problems in composite materials, A Fast High Order Method for the Time-Fractional Diffusion Equation, Post-processed Galerkin approximation of improved order for wave equations, The Stokes complex for Virtual Elements in three dimensions, Numerical algorithms for semilinear parabolic equations with small parameter based on approximation of stochastic equations, Error Estimates for Lagrange--Galerkin Approximation of American Options Valuation, A class of fully discrete approximations for the first order differential equations in banach spaces with uniform estimates on the whole of, A Minimal Stabilization Procedure for Isogeometric Methods on Trimmed Geometries, Coupling non-conforming discretizations of PDEs by spectral approximation of the Lagrange multiplier space, A Variable-Separation Method for Nonlinear Partial Differential Equations With Random Inputs, On Some Weighted Stokes Problems: Applications on Smagorinsky Models, Existence, uniqueness and numerical solution of a fractional PDE with integral conditions, Multidomain mixed variational analysis of transport flow through elastoviscoplastic porous media, Efficient Entropy Stable Gauss Collocation Methods, An Augmented Lagrangian Preconditioner for the 3D Stationary Incompressible Navier--Stokes Equations at High Reynolds Number, A conforming mixed finite element method for the Navier–Stokes/Darcy–Forchheimer coupled problem, PDE eigenvalue iterations with applications in two-dimensional photonic crystals, Finite element error analysis of surface Stokes equations in stream function formulation, A class of second order difference approximations for solving space fractional diffusion equations, Parallelizing the Kolmogorov-Fokker-Planck equation, Unnamed Item, Analysis of Control Volume Heterogeneous Multiscale Methods for Single Phase Flow in Porous Media, Rigorous FEM for One-Dimensional Burgers Equation, Optimal Control of Nonlinear Transport-Flow Mixed Variational Problems, A fast algorithm for Gaussian type quadrature formulae with mixed boundary conditions and some lumped mass spectral approximations, Analysis of a backward Euler-type scheme for Maxwell’s equations in a Havriliak–Negami dispersive medium, $L^2$-Stability Independent of Diffusion for a Finite Element--Finite Volume Discretization of a Linear Convection-Diffusion Equation, Multigrid Algorithms for $hp$-Discontinuous Galerkin Discretizations of Elliptic Problems, Pseudospectral Least Squares Method for Stokes--Darcy Equations, Reduced basis techniques for nonlinear conservation laws, NUMERICAL SOLVING UNSTEADY SPACE-FRACTIONAL PROBLEMS WITH THE SQUARE ROOT OF AN ELLIPTIC OPERATOR, BOUNDEDNESS IN A BIOFILM-CHEMOTAXIS MODEL IN EVOLVING POROUS MEDIA, Reduced Basis Approximation of Parametrized Advection-Diffusion PDEs with High Péclet Number, Temporal Second-Order Finite Difference Schemes for Variable-Order Time-Fractional Wave Equations, An Lp spaces-based mixed virtual element method for the two-dimensional Navier–Stokes equations, Stability and error analysis for a second-order approximation of 1D nonlocal Schrödinger equation under DtN-type boundary conditions, A Singularly Perturbed Boundary Value Problems with Fractional Powers of Elliptic Operators, A LOCAL PROJECTION STABILIZATION FOR CONVECTION–DIFFUSION–REACTION EQUATIONS USING BIORTHOGONAL SYSTEMS, Optimal control in heterogeneous domain decomposition methods, Well Posedness of Fully Coupled Fracture/Bulk Darcy Flow with XFEM, Unnamed Item, Guaranteed contraction of adaptive inexact hp-refinement strategies with realistic stopping criteria, Optimal resource allocation for spatiotemporal control of invasive species, Predators as a possible strategy for controlling a Xylella epidemic?, A finite-element toolbox for the simulation of solid-liquid phase-change systems with natural convection, Numerical analysis of finite element methods for the cardiac extracellular-membrane-intracellular model: Steklov–Poincaré operator and spatial error estimates, Unnamed Item, An augmented mixed FEM for the convective Brinkman-Forchheimer problem: \textit{a priori} and \textit{a posteriori} error analysis, New Banach spaces-based fully-mixed finite element methods for pseudostress-assisted diffusion problems, A novel error analysis of spectral method for the anomalous subdiffusion problems with multi-term time-fractional derivative, An Introductory Review on A Posteriori Error Estimation in Finite Element Computations, A space-time energetic BIE method for 3D elastodynamics: the Dirichlet case, Analysis of a momentum conservative <scp>mixed‐FEM</scp> for the stationary <scp>Navier–Stokes</scp> problem, Numerical analysis of a FEM based on a time-primitive of the electric field for solving a nonlinear transient eddy current problem, Convergence analysis of the splitting method to the nonlinear heat equation, Parallel finite-element codes for the simulation of two-dimensional and three-dimensional solid-liquid phase-change systems with natural convection, Mixed-primal methods for natural convection driven phase change with Navier-Stokes-Brinkman equations, On a certified VMS-Smagorinsky reduced basis model with LPS pressure stabilisation, Discontinuous Galerkin for the wave equation: a simplified a priori error analysis, Numerical Dynamics of Integrodifference Equations: Hierarchies of Invariant Bundles in L^p (Ω), High-Order Mixed Finite Element Variable Eddington Factor Methods, Structure-Preserving Finite-Element Schemes for the Euler-Poisson Equations, Least-squares methods with nonconforming finite elements for general second-order elliptic equations, A five-field mixed formulation for stationary magnetohydrodynamic flows in porous media, An overlapping domain decomposition method for the solution of parametric elliptic problems via proper generalized decomposition, Unconditionally convergent numerical method for the fractional activator–inhibitor system with anomalous diffusion, The fast method and convergence analysis of the fractional magnetohydrodynamic coupled flow and heat transfer model for the generalized second-grade fluid, On the design of global-in-time Newton-multigrid-pressure Schur complement solvers for incompressible flow problems, Existence and uniqueness of solutions of the equations of quasistatic electroporoelasticity, The numerical manifold method for harmonic wave propagation in unbounded domains, An optimisation-based domain-decomposition reduced order model for the incompressible Navier-Stokes equations, Stability and error estimates of high order BDF-LDG discretizations for the Allen-Cahn equation, Local discontinuous Galerkin schemes for an ultrasonic propagation equation with fractional attenuation, Dissipation-based WENO stabilization of high-order finite element methods for scalar conservation laws, An Effective Model for Biofilm Growth Made by Chemotactical Bacteria in Evolving Porous Media, A HDG method for elliptic problems with integral boundary condition: theory and applications, L ∞−ASYMPTOTIC BEHAVIOR OF A FINITE ELEMENT METHOD FOR A SYSTEM OF PARABOLIC QUASI-VARIATIONAL INEQUALITIES WITH NONLINEAR SOURCE TERMS, Exponent Splitting Schemes for Evolution Equations with Fractional Powers of Operators, A mixed FEM for the coupled Brinkman-Forchheimer/Darcy problem, Numerical analysis of nonlinear degenerate parabolic problems with application to eddy current models, A priori error estimates of Crank-Nicolson finite element method for parabolic optimal control problems, A Lagrange–Galerkin Scheme for First Order Mean Field Game Systems, On stabilized equal-order virtual element methods for the Navier-Stokes equations on polygonal meshes, The Morley-type virtual element method for the Navier-Stokes equations in stream-function form, Convergence of a continuous Galerkin method for hyperbolic-parabolic systems, Global well-posedness of a model for precipitating convection with hydrostatic pressure under fast autoconversion and rain evaporation conditions, A Discretize-then-Optimize Approach to PDE-Constrained Shape Optimization, Space-Time Reduced Basis Methods for Parametrized Unsteady Stokes Equations, A machine learning approach to enhance the SUPG stabilization method for advection-dominated differential problems, Existence and blow-up of solutions for a class of semilinear pseudo-parabolic equations with cone degenerate viscoelastic term, Accelerating the Uzawa Algorithm, Simplifying numerical solution of constrained PDE systems through involutive completion, Optimal control and numerical adaptivity for advection–diffusion equations, Analysis of a prototypical multiscale method coupling atomistic and continuum mechanics, Flux-upwind stabilization of the discontinuous Petrov–Galerkin formulation with Lagrange multipliers for advection-diffusion problems, DUAL-PRIMAL METHODS FOR THE CARDIAC BIDOMAIN MODEL, Stable nonconforming methods for the Stokes problem., Output bounds for reduced-order approximations of elliptic partial differential equations, Calibration of a Hybrid Local-Stochastic Volatility Stochastic Rates Model with a Control Variate Particle Method, A recent survey on computational techniques for solving singularly perturbed boundary value problems, On the numerical solution of linear evolution problems with an integral operator coefficient, Superconvergence analysis for Maxwell's equations in dispersive media, Role of the LBB condition in weak spectral projection methods, On the coupling of 3D and 1D Navier-Stokes equations for flow problems in compliant vessels, On the Hermite interpolation, GPU-acceleration of waveform relaxation methods for large differential systems, A Newton--Galerkin Method for Fluid Flow Exhibiting Uncertain Periodic Dynamics, A three dimensional finite element method for biological active soft tissue Formulation in cylindrical polar coordinates, A numerical study on Neumann-Neumann methods forhpapproximations on geometrically refined boundary layer meshes II. Three-dimensional problems, Adaptive regularization, linearization, and discretization and a posteriori error control for the two-phase Stefan problem, Thermoviscoplasticity at small strains, Well-posedness and discrete analysis for advection-diffusion-reaction in poroelastic media, $α$Setup-PCTL: An Adaptive Setup-Based Two-Level Preconditioner for Sequence of Linear Systems of Three-Temperature Energy Equations