Fronts propagating with curvature-dependent speed: algorithms based on Hamilton-Jacobi formulations
Journal of Computational Physics
A level set formulation of Eulerian interface capturing methods for incompressible fluid flows
Journal of Computational Physics
A PDE-based fast local level set method
Journal of Computational Physics
Regularization Techniques for Numerical Approximation of PDEs with Singularities
Journal of Scientific Computing
Numerical approximations of singular source terms in differential equations
Journal of Computational Physics
Discretization of Dirac delta functions in level set methods
Journal of Computational Physics
The numerical approximation of a delta function with application to level set methods
Journal of Computational Physics
Two methods for discretizing a delta function supported on a level set
Journal of Computational Physics
Geometric integration over irregular domains with application to level-set methods
Journal of Computational Physics
High order numerical methods to a type of delta function integrals
Journal of Computational Physics
Journal of Computational Physics
Finite difference methods for approximating Heaviside functions
Journal of Computational Physics
High order numerical methods to two dimensional delta function integrals in level set methods
Journal of Computational Physics
High Order Numerical Methods to Three Dimensional Delta Function Integrals in Level Set Methods
SIAM Journal on Scientific Computing
Hi-index | 31.46 |
We prove a rate of convergence theorem for approximations to certain integrals over codimension one manifolds in R^n. The type of manifold involved here is defined by the zero level set of a smooth mapping u:R^n@?R. Our approximations are based on the two finite difference methods for discretizing delta functions presented in [16]. We included a convergence proof in that paper, but only proved rates of convergence in some greatly simplified situations. Numerical experiments indicated that our two methods were at least first and second order accurate, respectively. In this note we prove those empirical convergence rates for the two algorithms under fairly general hypotheses.