Uniformly high order accurate essentially non-oscillatory schemes, 111
Journal of Computational Physics
Numerical solution of the Riemann problem for two-dimensional gas dynamics
SIAM Journal on Scientific Computing
Weighted essentially non-oscillatory schemes
Journal of Computational Physics
Adaptive multiresolution schemes for shock computations
Journal of Computational Physics
An adaptive Cartesian grid method for unsteady compressible flow in irregular regions
Journal of Computational Physics
Efficient implementation of weighted ENO schemes
Journal of Computational Physics
Capturing shock reflections: an improved flux formula
Journal of Computational Physics
Multiresolution Schemes for the Numerical Solution of 2-D Conservation Laws I
SIAM Journal on Scientific Computing
High resolution schemes for hyperbolic conservation laws
Journal of Computational Physics - Special issue: commenoration of the 30th anniversary
Solution of Two-Dimensional Riemann Problems of Gas Dynamics by Positive Schemes
SIAM Journal on Scientific Computing
An adaptive version of the immersed boundary method
Journal of Computational Physics
A solution-adaptive upwind scheme for ideal magnetohydrodynamics
Journal of Computational Physics
Point Value Multiscale Algorithms for 2D Compressible Flows
SIAM Journal on Scientific Computing
Fully adaptive multiresolution finite volume schemes for conservation laws
Mathematics of Computation
Adaptive Mesh Methods for One- and Two-Dimensional Hyperbolic Conservation Laws
SIAM Journal on Numerical Analysis
A flux-split algorithm applied to conservative models for multicomponent compressible flows
Journal of Computational Physics
Understanding the Shu–Osher Conservative Finite Difference Form
Journal of Scientific Computing
Numerical methods for hyperbolic equations on unstructured meshes
Numerical methods for hyperbolic equations on unstructured meshes
Fully Adaptive Multiscale Schemes for Conservation Laws Employing Locally Varying Time Stepping
Journal of Scientific Computing
An adaptive multiresolution scheme with local time stepping for evolutionary PDEs
Journal of Computational Physics
Applied Numerical Mathematics
Local adaptive mesh refinement for shock hydrodynamics
Journal of Computational Physics
Efficient implementation of essentially non-oscillatory shock-capturing schemes, II
Journal of Computational Physics
A semi-Lagrangian AMR scheme for 2D transport problems in conservation form
Journal of Computational Physics
Well-Balanced Adaptive Mesh Refinement for shallow water flows
Journal of Computational Physics
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Adaptive mesh refinement is nowadays a widely used tool in the numerical solution of hyperbolic partial differential equations. The algorithm is based on the numerical approximation of the solution of the equations on a hierarchical set of meshes with different resolutions. Among the different parts that compose an adaptive mesh refinement algorithm, the decision of which level of resolution is adequate for each part of the domain, i.e., the design of a refinement criterion, is crucial for the performance of the algorithm. In this work we analyze a refinement strategy based on interpolation errors, as a building block of a high order adaptive mesh refinement algorithm. We show that this technique, inspired by multiresolution algorithms, is competitive, in terms of the balance between accuracy of the solutions and computational time, against adaptation methods based on a gradient sensor.