Finite Element Output Bounds for a Stabilized Discretization of Incompressible Stokes Flow
We introduce a new method for computing a posteriori bounds on engineering outputs from finite element discretizations of the incompressible Stokes equations. The method results from recasting the output problem as a minimization statement without resorting to an error formulation. The minimization...
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| Format: | Article |
| Language: | en_US |
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2003
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| Online Access: | http://hdl.handle.net/1721.1/4003 |
| _version_ | 1811081058935898112 |
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| author | Peraire, Jaime Budge, Alexander M. |
| author_facet | Peraire, Jaime Budge, Alexander M. |
| author_sort | Peraire, Jaime |
| collection | MIT |
| description | We introduce a new method for computing a posteriori bounds on engineering outputs from finite element discretizations of the incompressible Stokes equations. The method results from recasting the output problem as a minimization statement without resorting to an error formulation. The minimization statement engenders a duality relationship which we solve approximately by Lagrangian relaxation. We demonstrate the method for a stabilized equal-order approximation of Stokes flow, a problem to which previous output bounding methods do not apply. The conceptual framework for the method is quite general and shows promise for application to stabilized nonlinear problems, such as Burger's equation and the incompressible Navier-Stokes equations, as well as potential for compressible flow problems. |
| first_indexed | 2024-09-23T11:41:00Z |
| format | Article |
| id | mit-1721.1/4003 |
| institution | Massachusetts Institute of Technology |
| language | en_US |
| last_indexed | 2024-09-23T11:41:00Z |
| publishDate | 2003 |
| record_format | dspace |
| spelling | mit-1721.1/40032019-04-12T08:08:41Z Finite Element Output Bounds for a Stabilized Discretization of Incompressible Stokes Flow Peraire, Jaime Budge, Alexander M. finite element stabilization output bounds error estimation stokes equations We introduce a new method for computing a posteriori bounds on engineering outputs from finite element discretizations of the incompressible Stokes equations. The method results from recasting the output problem as a minimization statement without resorting to an error formulation. The minimization statement engenders a duality relationship which we solve approximately by Lagrangian relaxation. We demonstrate the method for a stabilized equal-order approximation of Stokes flow, a problem to which previous output bounding methods do not apply. The conceptual framework for the method is quite general and shows promise for application to stabilized nonlinear problems, such as Burger's equation and the incompressible Navier-Stokes equations, as well as potential for compressible flow problems. Singapore-MIT Alliance (SMA) 2003-12-23T02:31:32Z 2003-12-23T02:31:32Z 2002-01 Article http://hdl.handle.net/1721.1/4003 en_US High Performance Computation for Engineered Systems (HPCES); 208735 bytes application/pdf application/pdf |
| spellingShingle | finite element stabilization output bounds error estimation stokes equations Peraire, Jaime Budge, Alexander M. Finite Element Output Bounds for a Stabilized Discretization of Incompressible Stokes Flow |
| title | Finite Element Output Bounds for a Stabilized Discretization of Incompressible Stokes Flow |
| title_full | Finite Element Output Bounds for a Stabilized Discretization of Incompressible Stokes Flow |
| title_fullStr | Finite Element Output Bounds for a Stabilized Discretization of Incompressible Stokes Flow |
| title_full_unstemmed | Finite Element Output Bounds for a Stabilized Discretization of Incompressible Stokes Flow |
| title_short | Finite Element Output Bounds for a Stabilized Discretization of Incompressible Stokes Flow |
| title_sort | finite element output bounds for a stabilized discretization of incompressible stokes flow |
| topic | finite element stabilization output bounds error estimation stokes equations |
| url | http://hdl.handle.net/1721.1/4003 |
| work_keys_str_mv | AT perairejaime finiteelementoutputboundsforastabilizeddiscretizationofincompressiblestokesflow AT budgealexanderm finiteelementoutputboundsforastabilizeddiscretizationofincompressiblestokesflow |