Convergence Analysis of the Nonoverlapping Robin--Robin Method for Nonlinear Elliptic Equations
DOI10.1137/21M1414942zbMath1493.65259arXiv2105.00649OpenAlexW3158127538MaRDI QIDQ3390685
Publication date: 25 March 2022
Published in: SIAM Journal on Numerical Analysis (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/2105.00649
convergencenonlinear elliptic equationSteklov-Poincaré operatornonoverlapping domain decompositionRobin-Robin method
Multigrid methods; domain decomposition for boundary value problems involving PDEs (65N55) Stability and convergence of numerical methods for boundary value problems involving PDEs (65N12) Degenerate elliptic equations (35J70) Applications of operator theory to differential and integral equations (47N20) Numerical solutions to equations with nonlinear operators (65J15)
Cites Work
- Finite element approximation of the Navier-Stokes equations
- Finite element error estimates for nonlinear elliptic equations of monotone type
- Quasi-norm error bounds for the finite element approximation of a non- Newtonian flow
- On the nonlinear domain decomposition method
- Convergence analysis of domain decomposition based time integrators for degenerate parabolic equations
- On the scalability of classical one-level domain-decomposition methods
- Analysis of parallel Schwarz algorithms for time-harmonic problems using block Toeplitz matrices
- Global and uniform convergence of subspace correction methods for some convex optimization problems
- The 2-Lagrange Multiplier Method Applied to Nonlinear Transmission Problems for the Richards Equation in Heterogeneous Soil with Cross Points
- Convergence Behaviour of Dirichlet–Neumann and Robin Methods for a Nonlinear Transmission Problem
- Spectral Analysis of Dirichlet–Neumann Operators and Optimized Schwarz Methods with Robin Transmission Conditions
- The Numerical Solution of Parabolic and Elliptic Differential Equations
- Non-overlapping Domain Decomposition for the Richards Equation via Superposition Operators
- Robin–Robin Domain Decomposition Methods for the Stokes–Darcy Coupling
- Direct Methods in the Theory of Elliptic Equations
- On the Equivalence of Transmission Problems in Nonoverlapping Domain Decomposition Methods for Quasilinear PDEs
- A Lions non-overlapping domain decomposition method for domains with an arbitrary interface
- Boundary regularity for solutions of degenerate elliptic equations
- Splitting Algorithms for the Sum of Two Nonlinear Operators
- Rate of Convergence of Some Space Decomposition Methods for Linear and Nonlinear Problems
- Generalizations and Accelerations of Lions' Nonoverlapping Domain Decomposition Method for Linear Elliptic PDE
- A Domain Decomposition Method with Coupled Transmission Conditions for the Optimal Control of Systems Governed by Elliptic Partial Differential Equations
- Optimal Convergence for the Implicit Space‐Time Discretization of Parabolic Systems with p‐Structure
- Measure Theory
- Optimized Schwarz Methods
- On the Optimal Convergence Rate of a Robin-Robin Domain Decomposition Method
- Nonlinear partial differential equations with applications
- Nonlinear elliptic problems with \(p\)-structure under mixed boundary value conditions in polyhedral domains.
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