Search Results - "Error bounds for initial value and initial-boundary value problems involving PDEs"

Energy stability and error estimate of the RKMK2e scheme for the extended Fisher–Kolmogorov equation: Energy stability and error estimate of the RKMK2e scheme for the extended Fisher-Kolmogorov equation

Authors: Haifeng Wang Yan Wang Hong Zhang et al.

Source: Applied Numerical Mathematics. 212:60-76

Subject Terms: Error bounds for initial value and initial-boundary value problems involving PDEs, global-in-time energy stability, Finite difference methods for initial value and initial-boundary value problems involving PDEs, extended Fisher-Kolmogorov equation, Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs, error analysis, stabilization RKMK2e scheme

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Access URL: https://zbmath.org/8018678
https://doi.org/10.1016/j.apnum.2025.01.014

Second-Order Flows for Approaching Stationary Points of a Class of Nonconvex Energies via Convex-Splitting Schemes: Second-order flows for approaching stationary points of a class of nonconvex energies via convex-splitting schemes

Authors: Haifan Chen Guozhi Dong José A. Iglesias et al.

Source: SIAM Journal on Scientific Computing. 47:A1604-A1627

Subject Terms: Numerical optimization and variational techniques, convergence, stationary point, Numerical Analysis (math.NA), convex-splitting scheme, nonconvex functional, Error bounds for initial value and initial-boundary value problems involving PDEs, Mathematics - Analysis of PDEs, Second-order semilinear hyperbolic equations, Optimization and Control (math.OC), 35Q90, 35L71, 65M15, 65K10, FOS: Mathematics, dissipative hyperbolic equation, Mathematics - Numerical Analysis, PDEs in connection with mathematical programming, second-order flow, Mathematics - Optimization and Control, Analysis of PDEs (math.AP)

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Access URL: http://arxiv.org/abs/2402.12173

Optimal L2 error estimates of two structure-preserving finite element methods for Schrödinger-Boussinesq equations: Optimal \(L^2\) error estimates of two structure-preserving finite element methods for Schrödinger-Boussinesq equations

Authors: Houchao Zhang Junjun Wang Xueran Gong

Source: Applied Numerical Mathematics. 211:193-210

Subject Terms: Error bounds for initial value and initial-boundary value problems involving PDEs, optimal error estimates, NLS equations (nonlinear Schrödinger equations), Schrödinger-Boussinesq (SBq) equations, finite element method, Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs, structure-preserving

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Energy Stable and Maximum Bound Principle Preserving Schemes for the \(\boldsymbol {Q}\)-Tensor Flow of Liquid Crystals: Energy stable and maximum bound principle preserving schemes for the \(Q\)-tensor flow of liquid crystals

Authors: Dianming Hou Xiaoli Li Zhonghua Qiao et al.

Source: SIAM Journal on Numerical Analysis. 63:854-880

Subject Terms: energy stability, Error bounds for initial value and initial-boundary value problems involving PDEs, error estimates, \(Q\)-tensor, FOS: Mathematics, Initial-boundary value problems for higher-order parabolic equations, liquid crystal, Mathematics - Numerical Analysis, Numerical Analysis (math.NA), Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs, maximum bound principle

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Access URL: http://arxiv.org/abs/2309.02657

Optimizing Coarse Propagators in Parareal Algorithms: Optimizing coarse propagators in parareal algorithms

Authors: Bangti Jin Qingle Lin Zhi Zhou

Source: SIAM Journal on Scientific Computing. 47:A735-A761

Subject Terms: Method of lines for initial value and initial-boundary value problems involving PDEs, convergence factor, single step integrator, Parallel numerical computation, Numerical Analysis (math.NA), Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs, Multistep, Runge-Kutta and extrapolation methods for ordinary differential equations, Error bounds for initial value and initial-boundary value problems involving PDEs, parareal algorithm, Finite difference methods for initial value and initial-boundary value problems involving PDEs, FOS: Mathematics, Mathematics - Numerical Analysis, Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs, parabolic problems

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Access URL: http://arxiv.org/abs/2311.15320
https://zbmath.org/8010023
https://doi.org/10.1137/23m1619733

Efficient Adaptive Time-Stepping for Nonlinear Reaction-Diffusion Equations Using Crank-Nicolson Mixed FEM and Proper Orthogonal Decomposition: Efficient adaptive time-stepping for nonlinear reaction-diffusion equations using Crank-Nicolson mixed FEM and proper orthogonal decomposition

Authors: Shehabeldeen, Nermeen M. El-Shehawey, Mohammad A. El-Sayed, Ahmed M. A. et al.

Source: Electronic Journal of Mathematical Analysis and Applications. 13:1-16

Subject Terms: Neumann boundary conditions, Error bounds for initial value and initial-boundary value problems involving PDEs, proper orthogonal decomposition, reaction-diffusion equations, Reaction-diffusion equations, Crank-Nicolson method, finite element method, adaptive time-stepping, Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs, Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs, Dirichlet boundary conditions

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Numerical treatment of singularly perturbed turning point problems with delay in time

Authors: Singh, Satpal Kumar, Devendra Vigo-Aguiar, J.

Source: Journal of Mathematical Chemistry. 63:1035-1064

Subject Terms: Finite difference methods for boundary value problems involving PDEs, Shishkin mesh, Stability and convergence of numerical methods for boundary value problems involving PDEs, turning point, time lag, Spline approximation, Error bounds for initial value and initial-boundary value problems involving PDEs, parameter-uniform convergence, Second-order parabolic equations, Finite difference methods for initial value and initial-boundary value problems involving PDEs, Mesh generation, refinement, and adaptive methods for ordinary differential equations, delay differential equation, Singular perturbations, turning point theory, WKB methods for ordinary differential equations, splines, Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs, singular perturbation, Singular perturbations in context of PDEs

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Access URL: https://zbmath.org/8018422
https://doi.org/10.1007/s10910-025-01707-y

Study of a New Low-Oscillating Second-Order All-Mach Number IMEX Finite Volume Scheme for the Full Euler Equations: Study of a new low-oscillating second-order all-Mach number IMEX finite volume scheme for the full Euler equations

Authors: Allegrini, P Vignal, Mh Vignal, Marie-Hélène

Contributors: Allegrini, P Vignal, Mh Vignal, Marie-Hélène

Source: SIAM Journal on Scientific Computing. 47:A268-A299

Subject Terms: high-order schemes, Asymptotic Preserving schemes, High-order schemes, [MATH] Mathematics [math], hyperbolic conservation laws, IMEX schemes, Error bounds for initial value and initial-boundary value problems involving PDEs, Finite volume methods for initial value and initial-boundary value problems involving PDEs, Hyperbolic conservation laws, Compressible fluids and gas dynamics, Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs, asymptotic preserving schemes, finite volumes, low Mach number limit, Low Mach number limit

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Numerical Approximation of Discontinuous Solutions of the Semilinear Wave Equation: Numerical approximation of discontinuous solutions of the semilinear wave equation

Authors: Jiachuan Cao Buyang Li Yanping Lin et al.

Source: SIAM Journal on Numerical Analysis. 63:214-238

Subject Terms: Smoothness and regularity of solutions to PDEs, high-/low-frequency decomposition, Oscillation, zeros of solutions, mean value theorems, etc. in context of PDEs, Numerical Analysis (math.NA), Series expansions (e.g., Taylor, Lidstone series, but not Fourier series), Error bounds for initial value and initial-boundary value problems involving PDEs, KdV equations (Korteweg-de Vries equations), error estimates, Numerical interpolation, semilinear wave equation, discontinuous solution, Finite difference methods for initial value and initial-boundary value problems involving PDEs, FOS: Mathematics, Mathematics - Numerical Analysis, Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs, low regularity, Numerical methods for discrete and fast Fourier transforms, numerical approximation

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Access URL: http://arxiv.org/abs/2312.10392
https://zbmath.org/7981229
https://doi.org/10.1137/24m1635879

Error analysis of the Lie splitting for semilinear wave equations with finite-energy solutions

Authors: Ruff, Maximilian Schnaubelt, Roland

Source: Discrete and Continuous Dynamical Systems. 45:2969-3008

Subject Terms: 65M15 (Primary) 35B33, 35L71, 65M12 (Secondary), Numerical Analysis (math.NA), Critical exponents in context of PDEs, energy-critical semilinear wave equation, Error bounds for initial value and initial-boundary value problems involving PDEs, Mathematics - Analysis of PDEs, Second-order semilinear hyperbolic equations, Lie splitting, FOS: Mathematics, Mathematics - Numerical Analysis, Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs, error analysis, discrete Strichartz estimates, Analysis of PDEs (math.AP)

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Access URL: http://arxiv.org/abs/2311.03245

Numerical approximation for stochastic nonlinear fractional diffusion equation driven by rough noise

Authors: Daxin Nie Jing Sun Weihua Deng

Source: ESAIM: Mathematical Modelling and Numerical Analysis. 59:389-418

Subject Terms: Numerical solutions to stochastic differential and integral equations, Smoothness and regularity of solutions to PDEs, finite element method, Fractional processes, including fractional Brownian motion, Numerical Analysis (math.NA), Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs, fractional Brownian sheet, Numerical quadrature and cubature formulas, Fractional partial differential equations, 01 natural sciences, Wong-Zakai approximation, Error bounds for initial value and initial-boundary value problems involving PDEs, stochastic fractional diffusion equation, Fractional derivatives and integrals, convolution quadrature, Finite difference methods for initial value and initial-boundary value problems involving PDEs, FOS: Mathematics, Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs, PDEs with randomness, stochastic partial differential equations, Mathematics - Numerical Analysis, 0101 mathematics, Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs, error analysis

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Access URL: http://arxiv.org/abs/2201.10897

Regularity Theory and Numerical Algorithm for the Time-Fractional Klein-Kramers Equation: Regularity theory and numerical algorithm for the time-fractional Klein-Kramers equation

Authors: Sun, Jing Nie, Daxin Deng, Weihua

Source: Journal of Computational Mathematics. 43:257-279

Subject Terms: Error bounds for initial value and initial-boundary value problems involving PDEs, convolution quadrature, regularity estimate, local discontinuous Galerkin method, Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs, time-fractional Klein-Kramers equation, Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs, Fractional partial differential equations, error analysis

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Structure-preserving finite element methods for computing dynamics of rotating Bose–Einstein condensates: Structure-preserving finite element methods for computing dynamics of rotating Bose-Einstein condensates

Authors: Li, Meng Wang, Junjun Guan, Zhen et al.

Source: ESAIM: Mathematical Modelling and Numerical Analysis. 59:519-552

Subject Terms: NLS equations (nonlinear Schrödinger equations), structure-preserving, Numerical Analysis (math.NA), Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs, rotating Bose-Einstein condensate, Error bounds for initial value and initial-boundary value problems involving PDEs, Time-dependent Schrödinger equations and Dirac equations, Finite difference methods for initial value and initial-boundary value problems involving PDEs, Quantum dynamics and nonequilibrium statistical mechanics (general), Statistical mechanics of superfluids, FOS: Mathematics, Closed and approximate solutions to the Schrödinger, Dirac, Klein-Gordon and other equations of quantum mechanics, finite element methods, Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs, Mathematics - Numerical Analysis, Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs, Gross-Pitaevskii equation, angular momentum rotation

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Access URL: http://arxiv.org/abs/2405.16827
https://zbmath.org/7989674
https://doi.org/10.1051/m2an/2024067

An Energy Stable Local Discontinuous Galerkin Method for a Binary Compressible Flow: An energy stable local discontinuous Galerkin method for a binary compressible flow

Authors: Sun, Hui Tian, Lulu Guo, Hui

Source: Advances in Applied Mathematics and Mechanics. 17:888-908

Subject Terms: binary compressible flow, Error bounds for initial value and initial-boundary value problems involving PDEs, Crank-Nicolson time integration method, energy-stable, local discontinuous Galerkin method, Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs

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WAN Discretization of PDEs: Best Approximation, Stabilization, and Essential Boundary Conditions: WAN discretization of PDEs: best approximation, stabilization, and essential boundary conditions

Authors: Silvia Bertoluzza Erik Burman Cuiyu He

Source: SIAM Journal on Scientific Computing. 46:C688-C715

Subject Terms: Cea's Lemma, pseudotime XNODE, Numerical optimization and variational techniques, Systems of nonlinear higher-order PDEs, Pseudo-time XNODE, Cea's lemma, Stability and convergence of numerical methods for boundary value problems involving PDEs, Error bounds for initial value and initial-boundary value problems involving PDEs, PDEs on manifolds, weak adversarial network, Numerical PDE, Numerical methods for partial differential equations, initial value and time-dependent initial-boundary value problems, Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs, Weak solutions to PDEs, Weak Adversarial Network, Artificial neural networks and deep learning

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Access URL: https://zbmath.org/7964724
https://doi.org/10.1137/23m1588196

A Second-Order, Global-in-Time Energy Stable Implicit-Explicit Runge–Kutta Scheme for the Phase Field Crystal Equation: A second-order, global-in-time energy stable implicit-explicit Runge-Kutta scheme for the phase field crystal equation

Authors: Hong Zhang Haifeng Wang Xueqing Teng

Source: SIAM Journal on Numerical Analysis. 62:2667-2697

Subject Terms: global-in-time energy stability, phase field crystal equation, linear stabilization, optimal rate convergence analysis, Multistep, Runge-Kutta and extrapolation methods for ordinary differential equations, Integro-partial differential equations, Error bounds for initial value and initial-boundary value problems involving PDEs, Finite difference methods for initial value and initial-boundary value problems involving PDEs, Spectral, collocation and related methods for boundary value problems involving PDEs, Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs, Crystals in solids, Statistical mechanics of crystals, implicit-explicit Runge-Kutta method, Spectral, collocation and related methods for initial value and initial-boundary value problems involving PDEs, PDEs in connection with statistical mechanics

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A two level approach for simulating Bose–Einstein condensates by Localized Orthogonal Decomposition: A two level approach for simulating Bose-Einstein condensates by localized orthogonal decomposition

Authors: Christian Döding Patrick Henning Johan Wärnegård

Source: ESAIM: Mathematical Modelling and Numerical Analysis. 58:2317-2349

Subject Terms: Bose-Einstein condensate, NLS equations (nonlinear Schrödinger equations), finite element method, dynamics, Numerical Analysis (math.NA), 01 natural sciences, Error bounds for initial value and initial-boundary value problems involving PDEs, FOS: Mathematics, Closed and approximate solutions to the Schrödinger, Dirac, Klein-Gordon and other equations of quantum mechanics, ground state, Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs, Mathematics - Numerical Analysis, 0101 mathematics, nonlinear Schrödinger equation, 35Q55, 65M60, 65M15, 81Q05, Gross-Pitaevskii equation

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Access URL: http://arxiv.org/abs/2212.07392
https://zbmath.org/7971357
https://doi.org/10.1051/m2an/2024040

A reduced-order two-grid method based on POD technique for the semilinear parabolic equation

Authors: Junpeng Song Hongxing Rui

Source: Applied Numerical Mathematics. 205:240-254

Subject Terms: reduced-order two-grid, error estimate, Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs, Mesh generation, refinement, and adaptive methods for boundary value problems involving PDEs, Error bounds for initial value and initial-boundary value problems involving PDEs, proper orthogonal decomposition, Multigrid methods, domain decomposition for initial value and initial-boundary value problems involving PDEs, degrees of freedom, Finite difference methods for initial value and initial-boundary value problems involving PDEs, semilinear parabolic equation, Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs, Numerical methods for partial differential equations, initial value and time-dependent initial-boundary value problems, Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs, Semilinear parabolic equations

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Access URL: https://zbmath.org/7901906
https://doi.org/10.1016/j.apnum.2024.07.012

Stability analysis and error estimation based on difference spectral approximation for Allen–Cahn equation in a circular domain: Stability analysis and error estimation based on difference spectral approximation for Allen-Cahn equation in a circular domain

Authors: Zhenlan Pan Jihui Zheng Jing An

Source: Mathematical Methods in the Applied Sciences. 48:3214-3232

Subject Terms: Error bounds for initial value and initial-boundary value problems involving PDEs, circular domain, differential spectral approximation, stability and error estimation, Spectral, collocation and related methods for boundary value problems involving PDEs, Allen-Cahn equation, Spectral, collocation and related methods for initial value and initial-boundary value problems involving PDEs

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Computational and analytical studies of a new nonlocal phase-field crystal model in two dimensions

Authors: Qiang Du Kai Wang Jiang Yang

Source: Mathematical Models and Methods in Applied Sciences. 34:2099-2139

Subject Terms: Fourier spectral methods, crystal lattices, Nonlinear higher-order PDEs, Numerical Analysis (math.NA), nonlocal phase-field crystal models, 01 natural sciences, Error bounds for initial value and initial-boundary value problems involving PDEs, grain boundary, FOS: Mathematics, Mathematical modeling or simulation for problems pertaining to statistical mechanics, Theoretical approximation of solutions to integral equations, Mathematics - Numerical Analysis, asymptotically compatible schemes, structure factor, 0101 mathematics, Statistical mechanics of crystals

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Access URL: http://arxiv.org/abs/2407.15156
https://zbmath.org/7938963
https://doi.org/10.1142/s0218202524500441