Stability Estimates for Hybrid Coupled Domain Decomposition Methods
Steinbach, Olaf.
Stability Estimates for Hybrid Coupled Domain Decomposition Methods [electronic resource] / by Olaf Steinbach. - VI, 126 p. online resource. - Lecture Notes in Mathematics, 1809 0075-8434 ; . - Lecture Notes in Mathematics, 1809 .
Preliminaries -- Sobolev Spaces: Saddle Point Problems; Finite Element Spaces; Projection Operators; Quasi Interpolation Operators -- Stability Results: Piecewise Linear Elements; Dual Finite Element Spaces; Higher Order Finite Element Spaces; Biorthogonal Basis Functions -- The Dirichlet-Neumann Map for Elliptic Problems: The Steklov-Poincare Operator; The Newton Potential; Approximation by Finite Element Methods; Approximation by Boundary Element Methods -- Mixed Discretization Schemes: Variational Methods with Approximate Steklov-Poincare Operators; Lagrange Multiplier Methods -- Hybrid Coupled Domain Decomposition Methods: Dirichlet Domain Decomposition Methods; A Two-Level Method; Three-Field Methods; Neumann Domain Decomposition Methods;Numerical Results; Concluding Remarks -- References.
Domain decomposition methods are a well established tool for an efficient numerical solution of partial differential equations, in particular for the coupling of different model equations and of different discretization methods. Based on the approximate solution of local boundary value problems either by finite or boundary element methods, the global problem is reduced to an operator equation on the skeleton of the domain decomposition. Different variational formulations then lead to hybrid domain decomposition methods. .
9783540362500
10.1007/b80164 doi
Mathematics.
Numerical analysis.
Differential equations, partial.
Applications of Mathematics.
Numerical Analysis.
Partial Differential Equations.
T57-57.97
519
Stability Estimates for Hybrid Coupled Domain Decomposition Methods [electronic resource] / by Olaf Steinbach. - VI, 126 p. online resource. - Lecture Notes in Mathematics, 1809 0075-8434 ; . - Lecture Notes in Mathematics, 1809 .
Preliminaries -- Sobolev Spaces: Saddle Point Problems; Finite Element Spaces; Projection Operators; Quasi Interpolation Operators -- Stability Results: Piecewise Linear Elements; Dual Finite Element Spaces; Higher Order Finite Element Spaces; Biorthogonal Basis Functions -- The Dirichlet-Neumann Map for Elliptic Problems: The Steklov-Poincare Operator; The Newton Potential; Approximation by Finite Element Methods; Approximation by Boundary Element Methods -- Mixed Discretization Schemes: Variational Methods with Approximate Steklov-Poincare Operators; Lagrange Multiplier Methods -- Hybrid Coupled Domain Decomposition Methods: Dirichlet Domain Decomposition Methods; A Two-Level Method; Three-Field Methods; Neumann Domain Decomposition Methods;Numerical Results; Concluding Remarks -- References.
Domain decomposition methods are a well established tool for an efficient numerical solution of partial differential equations, in particular for the coupling of different model equations and of different discretization methods. Based on the approximate solution of local boundary value problems either by finite or boundary element methods, the global problem is reduced to an operator equation on the skeleton of the domain decomposition. Different variational formulations then lead to hybrid domain decomposition methods. .
9783540362500
10.1007/b80164 doi
Mathematics.
Numerical analysis.
Differential equations, partial.
Applications of Mathematics.
Numerical Analysis.
Partial Differential Equations.
T57-57.97
519