A posteriori error estimates for nonconforming approximation of elliptic problems based on Helmholtz type decomposition of the error
Dr. Satyendra K. TomarJan. 22, 2008, 3:30 p.m. HF 136
In this talk we shall present our work on a new type of a posteriori error estimates for nonconforming approximations of elliptic problems. The method is based on two key steps: (1) Helmholtz decomposition of vector-valued ﬁelds, and (2) splitting the residual functional with the help of an appropriate integral identity. We decompose the error into the ”gradient” and ”divergence-free” parts using the Helmholtz decomposition . Following [3, 4] we then obtain computable two-sided bounds of the solutions of the resulting auxiliary problems. The estimates obtained differ from that was derived in [2, 5] using a projection to the conforming space. The numerical experiments conﬁrm that the a posteriori estimates derived with the help of Helmholtz decomposition are qualitatively same as those with projection arguments and can be efﬁciently exploited in practical computations.
Key words: Discontinuous Galerkin FEM; a posteriori error estimates; Helmholtz decomposition.
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