Abstract
Solving linear divergence-curl system with Dirichlet conditions is reduced to finding an unknown vector function in the space of piecewise-polynomial gradients of harmonic functions. In this approach one can use the boundary least squares method with a harmonic basis of a high order of approximation formulated by the authors previously. The justification of this method is given. The properties of the bilinear form and approximating properties of the basis are investigated. Convergence of approximate solutions is proved. A numerical example with estimates of experimental orders of convergence in
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© 2019 Walter de Gruyter GmbH, Berlin/Boston
Artikel in diesem Heft
- Frontmatter
- Efficient projection method for a system of differential equations of Fokker−Planck type
- Two variants of Monte Carlo projection method for numerical solution of nonlinear Boltzmann equation
- Subgrid modelling of convective diffusion in a multiscale random medium
- Solution method for underdetermined systems of nonlinear equations
- Boundary least squares method with three-dimensional harmonic basis of higher order for solving linear div-curl systems with Dirichlet conditions
Artikel in diesem Heft
- Frontmatter
- Efficient projection method for a system of differential equations of Fokker−Planck type
- Two variants of Monte Carlo projection method for numerical solution of nonlinear Boltzmann equation
- Subgrid modelling of convective diffusion in a multiscale random medium
- Solution method for underdetermined systems of nonlinear equations
- Boundary least squares method with three-dimensional harmonic basis of higher order for solving linear div-curl systems with Dirichlet conditions