A posteriori error analysis of the discontinuous finite element methods for first order hyperbolic problems |
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Authors: | Tie Zhang Nan Feng |
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Institution: | Department of Mathematics, Northeastern University, Shenyang 110004, China |
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Abstract: | In this paper, we consider the a posteriori error analysis of discontinuous Galerkin finite element methods for the steady and nonsteady first order hyperbolic problems with inflow boundary conditions. We establish several residual-based a posteriori error estimators which provide global upper bounds and a local lower bound on the error. Further, for nonsteady problem, we construct a fully discrete discontinuous finite element scheme and derive the a posteriori error estimators which yield global upper bound on the error in time and space. Our a posteriori error analysis is based on the mesh-dependent a priori estimates for the first order hyperbolic problems. These a posteriori error analysis results can be applied to develop the adaptive discontinuous finite element methods. |
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Keywords: | First order hyperbolic problem Discontinuous finite element method A posteriori error analysis |
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