Approximations of Very Weak Solutions to Boundary-Value Problems

@article{Berggren2004ApproximationsOV,
  title={Approximations of Very Weak Solutions to Boundary-Value Problems},
  author={Martin Berggren},
  journal={SIAM J. Numerical Analysis},
  year={2004},
  volume={42},
  pages={860-877}
}
Standard weak solutions to the Poisson problem on a bounded domain have squareintegrable derivatives, which limits the admissible regularity of inhomogeneous data. The concept of solution may be further weakened in order to define solutions when data is rough, such as for inhomogeneous Dirichlet data that is only square-integrable over the boundary. Such very weak solutions satisfy a nonstandard variational form (u, v) = G(v). A Galerkin approximation combined with an approximation of the right… CONTINUE READING
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