Anisotropic grid adaptation for Navier--Stokes' equations
Journal of Computational Physics
Accurate and stable grid interfaces for finite volume methods
Applied Numerical Mathematics
Preconditioned implicit solution of linear hyperbolic equations with adaptivity
Journal of Computational and Applied Mathematics
Space---Time Adaptive Solution of First Order PDES
Journal of Scientific Computing
Cost-effectiveness of fully implicit moving mesh adaptation: a practical investigation in 1D
Journal of Computational Physics
Implicit adaptive mesh refinement for 2D reduced resistive magnetohydrodynamics
Journal of Computational Physics
Adjoint correction and bounding of error using lagrange form of truncation term
Computers & Mathematics with Applications
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The steady state solution of the Euler equations of inviscid flow is computed by an adaptive method. The grid is structured and is refined and coarsened in predefined blocks. The equations are discretized by a finite volume method. Error equations, satisfied by the solution errors, are derived with the discretization error as the driving right-hand side. An algorithm based on the error equations is developed for errors propagated along streamlines. Numerical examples from two-dimensional compressible and incompressible flow illustrate the method.