Convergence analysis of spatially adaptive Rothe methods

DOI10.1007/s10208-013-9183-7zbMath1309.65107OpenAlexW2010668070MaRDI QIDQ486668

Petru A. Cioica, Ulrich Friedrich, Nicolas Döhring, Klaus Ritter, Thorsten Raasch, Felix Lindner, Stephan Dahlke, Stefan Kinzel, Rene L. Schilling

Publication date: 16 January 2015

Published in: Foundations of Computational Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s10208-013-9183-7

zbMATH Keywords

convergenceabstract Cauchy problemRothe's methodparabolic evolution equations\(s\)-stage linearly implicit methodsadaptive wavelet methodshorizontal method of lines

Mathematics Subject Classification ID

Nonlinear parabolic equations (35K55) Abstract parabolic equations (35K90) Numerical methods for wavelets (65T60) Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs (65M12) Method of lines for initial value and initial-boundary value problems involving PDEs (65M20) Numerical solutions to abstract evolution equations (65J08) Numerical solution of discretized equations for initial value and initial-boundary value problems involving PDEs (65M22)

Related Items

On the convergence analysis of the inexact linearly implicit Euler scheme for a class of stochastic partial differential equations, Numerical solution of parabolic problems based on a weak space-time formulation, An optimal adaptive tensor product wavelet solver of a space-time FOSLS formulation of parabolic evolution problems, Parallel space-time \(hp\) adaptive discretization scheme for parabolic problems

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Stable multiscale bases and local error estimation for elliptic problems
• Adaptive finite element methods in computational mechanics
• Semigroups of linear operators and applications to partial differential equations
• Wavelets with complementary boundary conditions -- functions spaces on the cube
• A posteriori error estimation and adaptive mesh-refinement techniques
• Adaptive multilevel solution of nonlinear parabolic PDE systems. Theory, algorithm, and applications
• Besov regularity for elliptic boundary value problems in polygonal domains
• Adaptive wavelet methods. II: Beyond the elliptic case
• Adaptive finite element methods with convergence rates
• The inhomogeneous Dirichlet problem in Lipschitz domains
• The wavelet element method. II: Realization and additional features in 2D and 3D
• Optimality of a standard adaptive finite element method
• Optimal approximation of elliptic problems by linear and nonlinear mappings. I
• Adaptive Finite Element Methods for Parabolic Problems I: A Linear Model Problem
• Some A Posteriori Error Estimators for Elliptic Partial Differential Equations
• On the Discretization in Time of Semilinear Parabolic Equations with Nonsmooth Initial Data
• Adaptive Finite Element Methods for Parabolic Problems VI: Analytic Semigroups
• A Second-Order Rosenbrock Method Applied to Photochemical Dispersion Problems
• Composite wavelet bases for operator equations
• AN ADAPTIVE FINITE ELEMENT METHOD WITH EFFICIENT MAXIMUM NORM ERROR CONTROL FOR ELLIPTIC PROBLEMS
• Besov regularity for elliptic boundary value problems
• Adaptive wavelet methods for elliptic operator equations: Convergence rates
• Adaptive Finite Element Methods for Parabolic Problems II: Optimal Error Estimates in $L_\infty L_2 $ and $L_\infty L_\infty $
• Linearly implicit time discretization of non-linear parabolic equations
• A Convergent Adaptive Algorithm for Poisson’s Equation
• A Posteriori Error Estimates for Elliptic Problems in Two and Three Space Dimensions
• Wavelets on Manifolds I: Construction and Domain Decomposition
• Adaptive frame methods for elliptic operator equations: the steepest descent approach
• Galerkin Finite Element Methods for Parabolic Problems
• On Besov regularity of solutions to nonlinear elliptic partial differential equations