Error Control, Adaptive Discretizations, and Applications, Volume 60, Part Three highlights new advances, with this volume presenting interesting chapters written by an international board of authors. Chapters in this release cover Higher order discontinuous Galerkin finite element methods for the contact problems, Anisotropic Recovery-Based Error Estimators and Mesh Adaptation Tailored for Real-Life Engineering Innovation, Adaptive mesh refinement on Cartesian meshes applied to the mixed finite element discretization of the multigroup neutron diffusion equations, A posteriori error analysis for Finite Element approximation of some groundwater models Part I: Linear models, A posteriori error estimates for low frequency electromagnetic computations, and more.
Other sections delve into A posteriori error control for stochastic Galerkin FEM with high-dimensional random parametric PDEs and Recovery techniques for finite element methods.
1. 1 Introduction to contact problem - p. 2 2. 2 Obstacle and Signorini problems - p. 3 3. 3 Discrete problem - p. 11 4. 4 Lagrange multipliers - p. 18 5. 5 A posteriori error analysis - p. 27 6. 6 Numerical experiments - p. 47 7. References - p. 51 8. Further reading - p. 53 9. Chapter Two: Practical use of metric-based anisotropic mesh adaptation for industrial applications - p. 57 10. Abstract - p. 57 11. 1 Introduction - p. 58 12. 2 Anisotropic mesh adaptation algorithms with mesh-convergence analysis - p. 60 13. 3 Continuous mesh framework - p. 65 14. 4 RANS error estimates - p. 70 15. 5 Mesh adaptation components - p. 81 16. 6 Numerical results - p. 86 17. 7 Conclusion and future works - p. 107 18. Acknowledgements - p. 108 19. References - p. 108 20. Chapter Three: Numerical analysis of variational-hemivariational inequalities with applications in contact mechanics - p. 113 21. Abstract - p. 114 22. 1 Introduction - p. 114 23. 2 Preliminaries - p. 116 24. 3 Sample problems from contact mechanics - p. 121 25. 4 Numerical analysis of an abstract variational-hemivariational inequality - p. 127 26. 5 Studies of the contact problems - p. 141 27. 6 Virtual element method for variational-hemivariational inequality - p. 148 28. 7 Virtual element method for contact problems - p. 155 29. 8 Numerical examples - p. 163 30. 9 Concluding remarks - p. 172 31. References - p. 173 32. Chapter Four: Recovery-based accuracy assessment of numerical analysis results in linear elasticity. A code for moving least squares recovery based on physics - p. 179 33. Chapter Five: Adaptive mesh refinement on Cartesian meshes applied to the mixed finite element discretization of the multigroup neutron diffusion equations - p. 201 34. Abstract - p. 202 35. 1 Introduction - p. 202 36. 2 Notations - p. 203 37. 3 The neutron diffusion model - p. 204 38. 4 Algorithmic motivations - p. 210 39. 5 A posteriori error estimators for a mixed finite element discretization - p. 213 40. 6 Adaptive mesh refinement - p. 218 41. 7 Numerical illustration - p. 219 42. 8 Conclusion - p. 228 43. Acknowledgements - p. 229 44. References - p. 233 45. Chapter Six: A posteriori error analysis for finite element approximation of some groundwater models Part I: Linear case - p. 235 46. Abstract - p. 235 47. 1 Introduction - p. 235 48. 2 Some porous media models - p. 238 49. 3 Finite element approximation - p. 241 50. 4 A posteriori analysis for linear elliptic problems - p. 248 51. 5 A posteriori analysis for linear parabolic problems - p. 281 52. References - p. 297 53. Chapter Seven: A posteriori error estimates for low frequency electromagnetic computations - p. 301 54. Chapter Eight: A posteriori error control for stochastic Galerkin FEM with high-dimensional random parametric PDEs - p. 347 55. Abstract - p. 348 56. 1 Introduction - p. 348 57. 2 Random field expansion and polynomial chaos - p. 351 58. 3 SGFEM for the parametric Poisson model problem - p. 358 59. 4 A posteriori error control - p. 367 60. 5 Adaptive refinement algorithm - p. 374 61. 6 Numerical experiments - p. 376 62. 7 Extension to log-normal coefficients - p. 385 63. 8 Summary and outlook - p. 392 64. References - p. 393 65. Chapter Nine: Recovery techniques for finite element methods - p. 399 66. Abstract - p. 399 67. 1 Introduction - p. 400 68. 2 Notations - p. 404 69. 3 Polynomial preserving recovery - p. 406 70. 4 Superconvergence analysis of recovery techniques - p. 422 71. 5 Recovery type a posteriori error estimators - p. 440 72. 6 Numerical illustrations - p. 446 73. 7 Conclusion - p. 456 74. Acknowledgments - p. 457 75. References - p. 457
Error Control, Adaptive Discretizations, and Applications, Volume 60, Part Three highlights new advances, with this volume presenting interesting chapters written by an international board of authors. Chapters in this release cover Higher order discontinuous Galerkin finite element methods for the contact problems, Anisotropic Recovery-Based Error Estimators and Mesh Adaptation Tailored for Real-Life Engineering Innovation, Adaptive mesh refinement on Cartesian meshes applied to the mixed finite element discretization of the multigroup neutron diffusion equations, A posteriori error analysis for Finite Element approximation of some groundwater models Part I: Linear models, A posteriori error estimates for low frequency electromagnetic computations, and more.
Other sections delve into A posteriori error control for stochastic Galerkin FEM with high-dimensional random parametric PDEs and Recovery techniques for finite element methods.
1. 1 Introduction to contact problem - p. 2 2. 2 Obstacle and Signorini problems - p. 3 3. 3 Discrete problem - p. 11 4. 4 Lagrange multipliers - p. 18 5. 5 A posteriori error analysis - p. 27 6. 6 Numerical experiments - p. 47 7. References - p. 51 8. Further reading - p. 53 9. Chapter Two: Practical use of metric-based anisotropic mesh adaptation for industrial applications - p. 57 10. Abstract - p. 57 11. 1 Introduction - p. 58 12. 2 Anisotropic mesh adaptation algorithms with mesh-convergence analysis - p. 60 13. 3 Continuous mesh framework - p. 65 14. 4 RANS error estimates - p. 70 15. 5 Mesh adaptation components - p. 81 16. 6 Numerical results - p. 86 17. 7 Conclusion and future works - p. 107 18. Acknowledgements - p. 108 19. References - p. 108 20. Chapter Three: Numerical analysis of variational-hemivariational inequalities with applications in contact mechanics - p. 113 21. Abstract - p. 114 22. 1 Introduction - p. 114 23. 2 Preliminaries - p. 116 24. 3 Sample problems from contact mechanics - p. 121 25. 4 Numerical analysis of an abstract variational-hemivariational inequality - p. 127 26. 5 Studies of the contact problems - p. 141 27. 6 Virtual element method for variational-hemivariational inequality - p. 148 28. 7 Virtual element method for contact problems - p. 155 29. 8 Numerical examples - p. 163 30. 9 Concluding remarks - p. 172 31. References - p. 173 32. Chapter Four: Recovery-based accuracy assessment of numerical analysis results in linear elasticity. A code for moving least squares recovery based on physics - p. 179 33. Chapter Five: Adaptive mesh refinement on Cartesian meshes applied to the mixed finite element discretization of the multigroup neutron diffusion equations - p. 201 34. Abstract - p. 202 35. 1 Introduction - p. 202 36. 2 Notations - p. 203 37. 3 The neutron diffusion model - p. 204 38. 4 Algorithmic motivations - p. 210 39. 5 A posteriori error estimators for a mixed finite element discretization - p. 213 40. 6 Adaptive mesh refinement - p. 218 41. 7 Numerical illustration - p. 219 42. 8 Conclusion - p. 228 43. Acknowledgements - p. 229 44. References - p. 233 45. Chapter Six: A posteriori error analysis for finite element approximation of some groundwater models Part I: Linear case - p. 235 46. Abstract - p. 235 47. 1 Introduction - p. 235 48. 2 Some porous media models - p. 238 49. 3 Finite element approximation - p. 241 50. 4 A posteriori analysis for linear elliptic problems - p. 248 51. 5 A posteriori analysis for linear parabolic problems - p. 281 52. References - p. 297 53. Chapter Seven: A posteriori error estimates for low frequency electromagnetic computations - p. 301 54. Chapter Eight: A posteriori error control for stochastic Galerkin FEM with high-dimensional random parametric PDEs - p. 347 55. Abstract - p. 348 56. 1 Introduction - p. 348 57. 2 Random field expansion and polynomial chaos - p. 351 58. 3 SGFEM for the parametric Poisson model problem - p. 358 59. 4 A posteriori error control - p. 367 60. 5 Adaptive refinement algorithm - p. 374 61. 6 Numerical experiments - p. 376 62. 7 Extension to log-normal coefficients - p. 385 63. 8 Summary and outlook - p. 392 64. References - p. 393 65. Chapter Nine: Recovery techniques for finite element methods - p. 399 66. Abstract - p. 399 67. 1 Introduction - p. 400 68. 2 Notations - p. 404 69. 3 Polynomial preserving recovery - p. 406 70. 4 Superconvergence analysis of recovery techniques - p. 422 71. 5 Recovery type a posteriori error estimators - p. 440 72. 6 Numerical illustrations - p. 446 73. 7 Conclusion - p. 456 74. Acknowledgments - p. 457 75. References - p. 457
