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A posteriori error analysis of a cell-centered finite volume method for semilinear elliptic problems |
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| Authors: | Don Estep Michael Pernice Du Pham Simon Tavener Haiying Wang |
| Affiliation: | aDepartment of Mathematics, Colorado State University, Fort Collins, CO 80524, USA;bDepartment of Statistics, Colorado State University, Fort Collins, CO 80524, USA;cIdaho National Laboratory, Idaho Falls, ID 83415, USA |
| Abstract: | In this paper, we conduct a goal-oriented a posteriori analysis for the error in a quantity of interest computed from a cell-centered finite volume scheme for a semilinear elliptic problem. The a posteriori error analysis is based on variational analysis, residual errors and the adjoint problem. To carry out the analysis, we use an equivalence between the cell-centered finite volume scheme and a mixed finite element method with special choice of quadrature. |
| Keywords: | A posteriori error analysis Adjoint problem Cell-centered finite volume method Convection– diffusion– reaction problem Mixed finite element method Quadrature error Residual error |
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