In this paper, we show how to couple the local discontinuous Galerkin method and the Raviart-Thomas mixed finite element method for elliptic equations modeling flow problems. We then show that the approximation of the velocity converges with the optimal order of k when we take the local discontinuous Galerkin that uses polynomials of degree k and the Raviart-Thomas space of polynomials of degree k-1.
Bibliographical noteFunding Information:
This work was funded in part by the National Science Foundation, project numbers DMS-9805491 and DMS-9873326. Bernardo Cockburn is partially supported by the National Science Foundation and the Minnesota Supercomputing Institute. Clint Dawson is partially supported by the National Science Foundation.
- Discontinuous Galerkin method
- Elliptic equations
- Mixed finite element method