Finite element approximations of the stochastic mean curvature flow of planar curves of graphs

DOI10.1007/s40072-014-0025-7zbMath1300.65006arXiv1303.5930OpenAlexW2042628437MaRDI QIDQ744174

Yukun Li, Andreas Prohl, Xiaobing Feng

Publication date: 6 October 2014

Published in: Stochastic and Partial Differential Equations. Analysis and Computations (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1303.5930

zbMATH Keywords

convergencefinite element methodregularizationnumerical exampleserror analysislevel set methodfully discretesemi-discretequasilinear parabolic stochastic partial differential equationstochastic mean curvature flow

Mathematics Subject Classification ID

Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs (65M12) Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs (65M60) Stochastic partial differential equations (aspects of stochastic analysis) (60H15) Error bounds for initial value and initial-boundary value problems involving PDEs (65M15) PDEs with randomness, stochastic partial differential equations (35R60) Computational methods for stochastic equations (aspects of stochastic analysis) (60H35) Numerical solutions to stochastic differential and integral equations (65C30) Method of lines for initial value and initial-boundary value problems involving PDEs (65M20) Quasilinear parabolic equations (35K59)

Related Items (11)

Weak solutions for a stochastic mean curvature flow of two-dimensional graphs ⋮ Finite element approximations of a class of nonlinear stochastic wave equations with multiplicative noise ⋮ Strong Convergence of a Fully Discrete Finite Element Method for a Class of Semilinear Stochastic Partial Differential Equations with Multiplicative Noise ⋮ Higher order time discretization method for a class of semilinear stochastic partial differential equations with multiplicative noise ⋮ Finite Element Methods for the Stochastic Allen--Cahn Equation with Gradient-type Multiplicative Noise ⋮ Analysis of the Morley element for the Cahn–Hilliard equation and the Hele-Shaw flow ⋮ Stochastic variational inequalities and regularity for degenerate stochastic partial differential equations ⋮ Convergence of finite element solutions of stochastic partial integro-differential equations driven by white noise ⋮ Some algorithms for the mean curvature flow under topological changes ⋮ Error analysis of a fully discrete Morley finite element approximation for the Cahn-Hilliard equation ⋮ Approximating Stochastic Evolution Equations with Additive White and Rough Noises

Cites Work

• Flow by mean curvature of convex surfaces into spheres
• Motion of level sets by mean curvature. I
• Mean curvature evolution of entire graphs
• Itô's formula for the \(L _{p }\)-norm of stochastic \({W^{1}_{p}}\)-valued processes
• Rate of convergence of space time approximations for stochastic evolution equations
• Fronts propagating with curvature-dependent speed: Algorithms based on Hamilton-Jacobi formulations
• Stochastic motion of mean curvature
• Convergence of the Allen-Cahn equation to Brakke's motion by mean curvature
• Minimal barriers for geometric evolutions
• Numerical analysis of the Allen-Cahn equation and approximation for mean curvature flows
• Uniqueness of motion by mean curvature perturbed by stochastic noise.
• Level set methods and dynamic implicit surfaces
• Finite-element-based discretizations of the incompressible Navier-Stokes equations with multiplicative random forcing
• Ergodicity of Stochastic Curve Shortening Flow in the Plane
• Finite-element approximation of the linearized Cahn-Hilliard-Cook equation
• Computation of geometric partial differential equations and mean curvature flow
• Phase transitions and generalized motion by mean curvature
• The Motion of a Surface by Its Mean Curvature. (MN-20)
• Fully nonlinear stochastic partial differential equations
• Fully nonlinear stochastic partial differential equations: non-smooth equations and applications
• Curvature-Driven Flows: A Variational Approach
• Rates of Convergence for Discretizations of the Stochastic Incompressible Navier--Stokes Equations
• The Mathematical Theory of Finite Element Methods
• Uniqueness and existence of viscosity solutions of generalized mean curvature flow equations
• Stochastic Equations in Infinite Dimensions
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