Error Control, Adaptive Discretizations, and Applications, Part Four, Volume 61 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, and more.
Other sections cover 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.
1. 1 Introduction - p. 2 2. 2 Decomposition of symmetric positive definite matrices - p. 10 3. 3 Scheme construction and variants - p. 29 4. 4 Numerical experiments - p. 56 5. 5 Conclusion - p. 64 6. References - p. 71 7. Chapter Two: Dual Weighted Residual-driven adaptive mesh refinement to enhance biomechanical simulations - p. 75 8. Chapter Three: Anisotropic recovery-based error estimators and mesh adaptation for real-life engineering innovation - p. 129 9. Chapter Four: Tree-based adaptive finite element methods for deformable image registration - p. 175 10. Chapter Five: Residual error estimators for Coulomb frictional contact - p. 207 11. Chapter Six: An introduction to the a posteriori error analysis of parabolic partial differential equations - p. 239 12. Chapter Seven: Parallel simulation and adaptive mesh refinement for 3D elastostatic contact mechanics problems between deformable bodies - p. 287 13. Chapter Eight: An posteriori error estimator for discontinuous Galerkin discretisations of convection-diffusion problems with application to Earth's mantle convection simulations - p. 347 14. Abstract - p. 347 15. 1 Introduction - p. 348 16. 2 The discontinuous Galerkin method for a model convection-diffusion problem - p. 352 17. 3 An a posteriori bound for stationary problems - p. 357 18. 4 A posteriori error analysis for the semi-discrete method - p. 374 19. 5 A posteriori error analysis for the fully-discrete scheme - p. 377 20. 6 Discussion and implementation of the estimators - p. 380 21. 7 Numerical experiments - p. 384 22. 8 The Boussinesq system and mantle convection simulations - p. 390 23. 9 Adaptive resolution of Boussinesq system - p. 394 24. 10 Conclusions - p. 401 25. References - p. 402 26. Chapter Nine: Optimal adaptive implicit time stepping - p. 407 27. Chapter Ten: A posteriori error analysis for finite element approximation of some groundwater models Part II: Richards equation and mixed finite element - p. 449 28. Abstract - p. 449 29. 1 Introduction - p. 449 30. 2 Mixed Finite element approximation - p. 454 31. 3 Residual a posteriori error estimate for linear problems - p. 462 32. 4 Residual a posteriori error estimate for nonlinear problems - p. 491 33. 5 Conclusion - p. 509 34. References - p. 510 35. Chapter Eleven: A posteriori error estimates and adaptivity for locally conservative methods - p. 513
Error Control, Adaptive Discretizations, and Applications, Part Four, Volume 61 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, and more.
Other sections cover 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.
1. 1 Introduction - p. 2 2. 2 Decomposition of symmetric positive definite matrices - p. 10 3. 3 Scheme construction and variants - p. 29 4. 4 Numerical experiments - p. 56 5. 5 Conclusion - p. 64 6. References - p. 71 7. Chapter Two: Dual Weighted Residual-driven adaptive mesh refinement to enhance biomechanical simulations - p. 75 8. Chapter Three: Anisotropic recovery-based error estimators and mesh adaptation for real-life engineering innovation - p. 129 9. Chapter Four: Tree-based adaptive finite element methods for deformable image registration - p. 175 10. Chapter Five: Residual error estimators for Coulomb frictional contact - p. 207 11. Chapter Six: An introduction to the a posteriori error analysis of parabolic partial differential equations - p. 239 12. Chapter Seven: Parallel simulation and adaptive mesh refinement for 3D elastostatic contact mechanics problems between deformable bodies - p. 287 13. Chapter Eight: An posteriori error estimator for discontinuous Galerkin discretisations of convection-diffusion problems with application to Earth's mantle convection simulations - p. 347 14. Abstract - p. 347 15. 1 Introduction - p. 348 16. 2 The discontinuous Galerkin method for a model convection-diffusion problem - p. 352 17. 3 An a posteriori bound for stationary problems - p. 357 18. 4 A posteriori error analysis for the semi-discrete method - p. 374 19. 5 A posteriori error analysis for the fully-discrete scheme - p. 377 20. 6 Discussion and implementation of the estimators - p. 380 21. 7 Numerical experiments - p. 384 22. 8 The Boussinesq system and mantle convection simulations - p. 390 23. 9 Adaptive resolution of Boussinesq system - p. 394 24. 10 Conclusions - p. 401 25. References - p. 402 26. Chapter Nine: Optimal adaptive implicit time stepping - p. 407 27. Chapter Ten: A posteriori error analysis for finite element approximation of some groundwater models Part II: Richards equation and mixed finite element - p. 449 28. Abstract - p. 449 29. 1 Introduction - p. 449 30. 2 Mixed Finite element approximation - p. 454 31. 3 Residual a posteriori error estimate for linear problems - p. 462 32. 4 Residual a posteriori error estimate for nonlinear problems - p. 491 33. 5 Conclusion - p. 509 34. References - p. 510 35. Chapter Eleven: A posteriori error estimates and adaptivity for locally conservative methods - p. 513
