An adaptive method with rigorous error control for the Hamilton–Jacobi equations. Part I: The one-dimensional steady state case☆
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2009, Applied Mathematical ModellingAn adaptive high-order discontinuous Galerkin method with error control for the Hamilton-Jacobi equations. Part I: The one-dimensional steady state case
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2006, Applied Numerical MathematicsAn adaptive method with rigorous error control for the Hamilton-Jacobi equations. Part II: The two-dimensional steady-state case
2005, Journal of Computational PhysicsCitation Excerpt :But first, we begin by defining the viscosity solution of the problem under consideration. In this paper, we have extended the adaptive method proposed in [4] to two-dimensional steady-state Hamilton–Jacobi equations. The method has been shown to guarantee a rigorous error control and to be extremely reliable and efficient for a wide variation of the tolerance parameter even in the presence of kinks in the viscosity solution with non-convex Hamiltonians.
Local a posteriori error estimates for time-dependent Hamilton-Jacobi equations
2013, Mathematics of ComputationAn optimal L<sup>1</sup>-minimization algorithm for stationary Hamilton-Jacobi equations
2009, Communications in Mathematical Sciences
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Partially supported by the National Science Foundation (Grant DMS-0107609) and by the University of Minnesota Supercomputer Institute.
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