A Second-Order Stabilization Method for Linearizing and Decoupling Nonlinear Parabolic Systems

DOI10.1137/19M1296136zbMath1453.65226OpenAlexW3091010697MaRDI QIDQ4970515

Guanyu Zhou, Yuki Ueda, Buyang Li

Publication date: 14 October 2020

Published in: SIAM Journal on Numerical Analysis (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1137/19m1296136

zbMATH Keywords

convergencestabilizationlinearizationdecouplingnonlinear parabolic system

Mathematics Subject Classification ID

Finite difference methods for initial value and initial-boundary value problems involving PDEs (65M06) Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs (65M12) Nonlinear initial, boundary and initial-boundary value problems for nonlinear parabolic equations (35K61) Flows related to mean curvature (53E10)

Related Items

The convergence analysis of semi- and fully-discrete projection-decoupling schemes for the generalized Newtonian models ⋮ Optimal error estimates of a lowest-order Galerkin-mixed FEM for the thermoviscoelastic Joule heating equations

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Nonlinear total variation based noise removal algorithms
• A gradient flow approach to large deviations for diffusion processes
• A linear finite volume method for nonlinear cross-diffusion systems
• On the convergence of multistep methods for nonlinear stiff differential equations
• Fully implicit, linearly implicit and implicit-explicit backward difference formulae for quasi-linear parabolic equations
• Non-parametric mean curvature evolution with boundary conditions
• Convergence of Runge-Kutta methods for nonlinear parabolic equations
• Image registration by a regularized gradient flow. A streaming implementation in DX9 graphics hardware
• Runge-Kutta time discretization of nonlinear parabolic equations studied via discrete maximal parabolic regularity
• A level set formulation for Willmore flow
• Optimal transport for applied mathematicians. Calculus of variations, PDEs, and modeling
• THE GEOMETRY OF DISSIPATIVE EVOLUTION EQUATIONS: THE POROUS MEDIUM EQUATION
• Moving Interfaces and Quasilinear Parabolic Evolution Equations
• Simple and Efficient ALE Methods with Provable Temporal Accuracy up to Fifth Order for the Stokes Equations on Time Varying Domains
• Error analysis of linearized semi-implicit Galerkin finite element methods for nonlinear parabolic equations
• An Introduction to the Regularity Theory for Elliptic Systems, Harmonic Maps and Minimal Graphs
• Computation of geometric partial differential equations and mean curvature flow
• Finite-Element Approximation of the Nonstationary Navier–Stokes Problem. Part IV: Error Analysis for Second-Order Time Discretization
• Finite Element Approximation of a Parabolic Integro-Differential Equation with a Weakly Singular Kernel
• Analysis of total variation flow and its finite element approximations
• On approximations of the curve shortening flow and of the mean curvature flow based on the DeTurck trick
• Convergence and Error Analysis for the Scalar Auxiliary Variable (SAV) Schemes to Gradient Flows
• Runge-Kutta Approximation of Quasi-Linear Parabolic Equations
• NUMERICAL GRADIENT FLOW DISCRETIZATION OF VISCOUS THIN FILMS ON CURVED GEOMETRIES
• Nonlinear diffusion equations with variable coefficients as gradient flows in Wasserstein spaces
• Linearized FE Approximations to a Nonlinear Gradient Flow
• Stability of Implicit-Explicit Backward Difference Formulas For Nonlinear Parabolic Equations

This page was built for publication: A Second-Order Stabilization Method for Linearizing and Decoupling Nonlinear Parabolic Systems