Nonlinear discontinuous Petrov–Galerkin methods
The discontinuous Petrov–Galerkin method is a minimal residual method with broken test spaces and is introduced for a nonlinear model problem in this paper. Its lowest-order version applies to a nonlinear uniformly convex model example and is equivalently characterized as a mixed formulation, a redu...
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| Veröffentlicht in: | Numerische Mathematik 2018-07, Vol.139 (3), p.529-561 |
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| container_title | Numerische Mathematik |
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| creator | Carstensen, C. Bringmann, P. Hellwig, F. Wriggers, P. |
| description | The discontinuous Petrov–Galerkin method is a minimal residual method with broken test spaces and is introduced for a nonlinear model problem in this paper. Its lowest-order version applies to a nonlinear uniformly convex model example and is equivalently characterized as a mixed formulation, a reduced formulation, and a weighted nonlinear least-squares method. Quasi-optimal a priori and reliable and efficient a posteriori estimates are obtained for the abstract nonlinear dPG framework for the approximation of a regular solution. The variational model example allows for a built-in guaranteed error control despite inexact solve. The subtle uniqueness of discrete minimizers is monitored in numerical examples. |
| doi_str_mv | 10.1007/s00211-018-0947-5 |
| format | Article |
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| subjects | Galerkin method Least squares method Mathematical analysis Mathematical and Computational Engineering Mathematical and Computational Physics Mathematical Methods in Physics Mathematics Mathematics and Statistics Numerical Analysis Numerical and Computational Physics Simulation Test procedures Theoretical |
| title | Nonlinear discontinuous Petrov–Galerkin methods |
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