Adaptive finite element methods for conservation laws based on a posteriori error estimates

• We prove a posteriori error estimates for a finite element method for systems of strictly hyperbolic conservation laws in one space dimension, and design corresponding adaptive methods. The proof of the a posteriori error estimates is based on a strong stability estimate for an associated dual problem, together with the Galerkin orthogonality of the finite-element method. The strong stability estimate uses the entropy condition for the system in an essential way.

Nyckelord

CONVECTION-DIFFUSION PROBLEMS

SHOCK PROFILES

CONVERGENCE

STABILITY

EQUATIONS

WAVES

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