A multiscale discontinuous Galerkin method with the computational structure of a continuous Galerkin method. (English) Zbl 1124.76027
Summary: Proliferation of degrees of freedom has plagued discontinuous Galerkin methodology from its inception over 30 years ago. This paper develops a new computational formulation that combines the advantages of discontinuous Galerkin methods with the data structure of their continuous Galerkin counterparts. The new method uses local, element-wise problems to project a continuous finite element space into a given discontinuous space, and then applies a discontinuous Galerkin formulation. The projection leads to parameterization of the discontinuous degrees of freedom by their continuous counterparts and has a variational multiscale interpretation. This significantly reduces the computational burden and, at the same time, little or no degradation of the solution occurs. In fact, the new method produces improved solutions compared with the traditional discontinuous Galerkin method in some situations.
MSC:
| 76M10 | Finite element methods applied to problems in fluid mechanics |
| 76R99 | Diffusion and convection |
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