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Numerical error estimation for nonlinear hyperbolic PDEs via nonlinear error transport
- Source :
- Computer Methods in Applied Mechanics and Engineering. :1-15
- Publication Year :
- 2012
- Publisher :
- Elsevier BV, 2012.
-
Abstract
- The estimation of discretization error in numerical simulations is a key component in the development of uncertainty quantification. In particular, there exists a need for reliable, robust estimators for finite volume and finite difference discretizations of hyperbolic partial differential equations. The approach espoused here, often called the error transport approach in the literature, is to solve an auxiliary error equation concurrently with the primal governing equation to obtain a point-wise (cell-wise) estimate of the discretization error. Nonlinear, time-dependent problems are considered. In contrast to previous work, fully nonlinear error equations are advanced, and potential benefits are identified. A systematic approach to approximate the local residual for both method-of-lines and space–time discretizations is developed. Behavior of the error estimates on problems that include weak solutions demonstrates the positive properties of nonlinear error transport.
- Subjects :
- Truncation error
Partial differential equation
Mechanical Engineering
Mathematical analysis
Computational Mechanics
Finite difference method
General Physics and Astronomy
Estimator
Residual
Computer Science Applications
Nonlinear system
Mechanics of Materials
Round-off error
Hyperbolic partial differential equation
Mathematics
Subjects
Details
- ISSN :
- 00457825
- Database :
- OpenAIRE
- Journal :
- Computer Methods in Applied Mechanics and Engineering
- Accession number :
- edsair.doi...........32534e49f49975bc2f6fe15d6af1b652