Journal of Computational Physics
Journal of Computational Physics
Multidomain WENO Finite Difference Method with Interpolation at Subdomain Interfaces
Journal of Scientific Computing
High-order semi-discrete central-upwind schemes for multi-dimensional Hamilton--Jacobi equations
Journal of Computational Physics
Numerical methods for high dimensional Hamilton-Jacobi equations using radial basis functions
Journal of Computational Physics
Hermite WENO schemes for Hamilton-Jacobi equations
Journal of Computational Physics
A TVD-type method for 2D scalar Hamilton-Jacobi equations on unstructured meshes
Journal of Computational and Applied Mathematics - Special issue: The international symposium on computing and information (ISCI2004)
Applied Numerical Mathematics - Numerical methods for viscosity solutions and applications
WENO schemes with Lax-Wendroff type time discretizations for Hamilton-Jacobi equations
Journal of Computational and Applied Mathematics
A discontinuous Galerkin finite element method for directly solving the Hamilton-Jacobi equations
Journal of Computational Physics
A variational approach to Eulerian geometry processing
ACM SIGGRAPH 2007 papers
A second order discontinuous Galerkin fast sweeping method for Eikonal equations
Journal of Computational Physics
Journal of Scientific Computing
A Second Order Central Scheme for Hamilton-Jacobi Equations on Triangular Grids
Numerical Analysis and Its Applications
Journal of Computational Physics
Journal of Scientific Computing
Adaptation of Eikonal Equation over Weighted Graph
SSVM '09 Proceedings of the Second International Conference on Scale Space and Variational Methods in Computer Vision
On the Numerical Approximation of First-Order Hamilton-Jacobi Equations
International Journal of Applied Mathematics and Computer Science - Scientific Computation for Fluid Mechanics and Hyperbolic Systems
A Central Discontinuous Galerkin Method for Hamilton-Jacobi Equations
Journal of Scientific Computing
Journal of Scientific Computing
A local discontinuous Galerkin method for directly solving Hamilton-Jacobi equations
Journal of Computational Physics
A Speed-Up Strategy for Finite Volume WENO Schemes for Hyperbolic Conservation Laws
Journal of Scientific Computing
Efficient algorithms for image and high dimensional data processing using eikonal equation on graphs
ISVC'10 Proceedings of the 6th international conference on Advances in visual computing - Volume Part II
A boundary-only meshless method for numerical solution of the Eikonal equation
Computational Mechanics
A Discontinuous Galerkin Solver for Front Propagation
SIAM Journal on Scientific Computing
Uniformly Accurate Discontinuous Galerkin Fast Sweeping Methods for Eikonal Equations
SIAM Journal on Scientific Computing
Computers & Mathematics with Applications
Binary weighted essentially non-oscillatory (BWENO) approximation
Journal of Computational and Applied Mathematics
The Chebyshev spectral viscosity method for the time dependent Eikonal equation
Mathematical and Computer Modelling: An International Journal
A Robust Reconstruction for Unstructured WENO Schemes
Journal of Scientific Computing
An Adaptive Sparse Grid Semi-Lagrangian Scheme for First Order Hamilton-Jacobi Bellman Equations
Journal of Scientific Computing
Hermite WENO schemes for Hamilton-Jacobi equations on unstructured meshes
Journal of Computational Physics
Alternating evolution discontinuous Galerkin methods for Hamilton-Jacobi equations
Journal of Computational Physics
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In this paper we construct high-order weighted essentially nonoscillatory (WENO) schemes for solving the nonlinear Hamilton--Jacobi equations on two-dimensional unstructured meshes. The main ideas are nodal based approximations, the usage of monotone Hamiltonians as building blocks on unstructured meshes, nonlinear weights using smooth indicators of second and higher derivatives, and a strategy to choose diversified smaller stencils to make up the bigger stencil in the WENO procedure. Both third-order and fourth-order WENO schemes using combinations of second-order approximations with nonlinear weights are constructed. Extensive numerical experiments are performed to demonstrate the stability and accuracy of the methods. High-order accuracy in smooth regions, good resolution of derivative singularities, and convergence to viscosity solutions are observed.