Error Control, Adaptive Discretizations, and Applications, Volume 59, Part Two highlights new advances in the field, with this new volume presenting interesting chapters written by an international board of authors. Chapters in this release cover hp adaptive Discontinuous Galerkin strategies driven by a posteriori error estimation with application to aeronautical flow problems,
An anisotropic mesh adaptation method based on gradient recovery and optimal shape elements, and Model reduction techniques for parametrized nonlinear partial differential equations.
1. 1 Introduction - p. 20 2. 2 Notation, abstract setting, finite element discretization - p. 25 3. 3 Single-goal oriented error control - p. 27 4. 4 Error estimation for non-standard discretizations - p. 53 5. 5 Multi-goal oriented error control - p. 64 6. 6 Applications - p. 69 7. 7 Conclusions and outlook - p. 96 8. Acknowledgments - p. 97 9. References - p. 97 10. Chapter Three: Parameter optimization for elliptic-parabolic systems by an adaptive trust-region reduced basis method - p. 109 11. Abstract - p. 109 12. 1 Introduction - p. 110 13. 2 The coupled elliptic-parabolic PDE - p. 112 14. 3 The discretization - p. 116 15. 4 Hierarchical a-posteriori error estimate for the state equation - p. 120 16. 5 The parameter optimization - p. 130 17. 6 Conclusions - p. 137 18. References - p. 143 19. Chapter Four: Iterative solvers in adaptive FEM: Adaptivity yields quasi-optimal computational runtime - p. 147 20. Abstract - p. 148 21. 1 Motivation - p. 148 22. 2 Adaptive mesh-refining algorithm - p. 152 23. 3 Numerical experiments - p. 166 24. 4 Convergence analysis - p. 173 25. 5 Extension 1: Goal-oriented adaptivity - p. 182 26. 6 Extension 2: Non-symmetric problems - p. 187 27. 7 Extension 3: Non-linear problems - p. 197 28. 8 Further generalizations and comments - p. 207 29. Acknowledgments - p. 208 30. References - p. 208 31. Chapter Five: Extending h adaptivity with refinement patterns - p. 213 32. Chapter Six: On the accuracy and efficiency of reduced order models: Towards real-world applications - p. 245 33. Chapter Seven: A posteriori error control and mesh adaptation for turbulence - p. 289 34. Chapter Eight: Model verification, updating, and selection from the constitutive relation error concept - p. 311 35. Abstract - p. 312 36. 1 Introduction - p. 312 37. 2 Model verification with the CRE concept - p. 316 38. 3 Goal-oriented error estimation with the CRE concept - p. 329 39. 4 Model updating with the CRE concept - p. 338 40. 5 Model selection with the CRE concept - p. 349 41. Funding & acknowledgments - p. 353 42. References - p. 353
Error Control, Adaptive Discretizations, and Applications, Volume 59, Part Two highlights new advances in the field, with this new volume presenting interesting chapters written by an international board of authors. Chapters in this release cover hp adaptive Discontinuous Galerkin strategies driven by a posteriori error estimation with application to aeronautical flow problems,
An anisotropic mesh adaptation method based on gradient recovery and optimal shape elements, and Model reduction techniques for parametrized nonlinear partial differential equations.
1. 1 Introduction - p. 20 2. 2 Notation, abstract setting, finite element discretization - p. 25 3. 3 Single-goal oriented error control - p. 27 4. 4 Error estimation for non-standard discretizations - p. 53 5. 5 Multi-goal oriented error control - p. 64 6. 6 Applications - p. 69 7. 7 Conclusions and outlook - p. 96 8. Acknowledgments - p. 97 9. References - p. 97 10. Chapter Three: Parameter optimization for elliptic-parabolic systems by an adaptive trust-region reduced basis method - p. 109 11. Abstract - p. 109 12. 1 Introduction - p. 110 13. 2 The coupled elliptic-parabolic PDE - p. 112 14. 3 The discretization - p. 116 15. 4 Hierarchical a-posteriori error estimate for the state equation - p. 120 16. 5 The parameter optimization - p. 130 17. 6 Conclusions - p. 137 18. References - p. 143 19. Chapter Four: Iterative solvers in adaptive FEM: Adaptivity yields quasi-optimal computational runtime - p. 147 20. Abstract - p. 148 21. 1 Motivation - p. 148 22. 2 Adaptive mesh-refining algorithm - p. 152 23. 3 Numerical experiments - p. 166 24. 4 Convergence analysis - p. 173 25. 5 Extension 1: Goal-oriented adaptivity - p. 182 26. 6 Extension 2: Non-symmetric problems - p. 187 27. 7 Extension 3: Non-linear problems - p. 197 28. 8 Further generalizations and comments - p. 207 29. Acknowledgments - p. 208 30. References - p. 208 31. Chapter Five: Extending h adaptivity with refinement patterns - p. 213 32. Chapter Six: On the accuracy and efficiency of reduced order models: Towards real-world applications - p. 245 33. Chapter Seven: A posteriori error control and mesh adaptation for turbulence - p. 289 34. Chapter Eight: Model verification, updating, and selection from the constitutive relation error concept - p. 311 35. Abstract - p. 312 36. 1 Introduction - p. 312 37. 2 Model verification with the CRE concept - p. 316 38. 3 Goal-oriented error estimation with the CRE concept - p. 329 39. 4 Model updating with the CRE concept - p. 338 40. 5 Model selection with the CRE concept - p. 349 41. Funding & acknowledgments - p. 353 42. References - p. 353
