On the Convergence of a Finite Element Method for a Nonlinear Hyperbolic Conservation Law

@inproceedings{Johnson2010OnTC,
  title={On the Convergence of a Finite Element Method for a Nonlinear Hyperbolic Conservation Law},
  author={Claes Johnson and Anders Szepessy},
  year={2010}
}
We consider a space-time finite element discretization of a time-dependent nonlinear hyperbolic conservation law in one space dimension (Burgers' equation). The finite element method is higher-order accurate and is a Petrov-Galerkin method based on the so-called streamline diffusion modification of the test functions giving added stability. We first prove that if a sequence of finite element solutions converges boundedly almost everywhere (as the mesh size tends to zero) to a function u, then u… CONTINUE READING

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