Error estimates and automatic time step control for nonlinear parabolic problems, I

Keywords

Mathematics, Discretization, Piecewise, Nonlinear system, Galerkin method

References

• An adaptive finite element method for linear elliptic problemsKenneth Eriksson, Claes Johnson — 1988
• Time discretization of parabolic problems by the discontinuous Galerkin methodKenneth Eriksson, Claes Johnson, Vidar Thomée — 1985
• Optimal Error Estimates and Adaptive Time and Space Step Control for Linear Parabolic ProblemsK. Eriksson, Claes Johnson, J. Lennblad — 1987

Cited by

• Modélisation tridimensionnelle par éléments finis pour l'analyse thermo-mécanique du refroidissement des pièces couléesOlivier Jaouen — 1998
• Reduced--Basis Output Bound Methods for Parametrized Partial Differential EquationsPrud'homme, C., Rovas, D.V., Veroy, K. — 2002
• Verification and Validation in Scientific ComputingWilliam L. Oberkampf, Christopher J. Roy — 2010
• Galerkin Finite Element Method by Using Bivariate Splines for Parabolic PDEsKai Qu, Bo Jiang — 2013
• Two-grid hp-version discontinuous Galerkin finite element methods for quasilinear PDEsScott Congreve — 2014
• Time discretisation of monotone nonlinear evolution problems by the discontinuous Galerkin methodEtienne Emmrich — 2011
• A LEAST SQUARES FORMULATION FOR SOLIDIFICATION PROCESSES: EXPERIMENTAL VALIDATIONS AND NUMERICAL SIMULATIONSKumar K. Tamma, Tianhong Ouyang — 1998
• hp-discontinuous Galerkin time stepping for parabolic problemsT. Werder, K. Gerdes, Dominik Schötzau — 2001
• Analysis of a robust finite element approximation for a parabolic equation with rough boundary dataDonald A. French, J. Thomas King — 1993
• Continuous finite elements in space and time for the heat equationA. K. Aziz, Peter Monk — 1989
• A tutorial in elementary finite element error analysis: A systematic presentation of a priori and a posteriori error estimatesJ.R. Stewart, Thomas J.R. Hughes — 1998
• Time finite element methods for structural dynamicsGregory M. Hulbert — 1992
• Comparison between the Discretized Continuous Gradient and the Discrete Gradient when Dealing with Nonlinear Parabolic ProblemsYann Favennec — 2005
• Local discontinuous Galerkin approximations to Richards’ equationH. Li, Matthew W. Farthing, Clint Dawson — 2007
• Review of code and solution verification procedures for computational simulationChristopher J. Roy — 2005
• Finite element approximation of a nonlinear heat conduction problem in anisotropic mediaMichal Křı́žek, L. Liu — 1998
• Space-time finite element methods for elastodynamics: formulations and error estimatesThomas J.R. Hughes, Gregory M. Hulbert — 1988
• A moving grid finite‐element method using grid deformationBill Semper, Guojun Liao — 1995
• A subdomain residual method for a posteriori error estimates of finite element solutions of viscoelastic fluid flowsHao Jin — 1996
• Variational analysis for simulating free-surface flows in a porous mediumShabbir Ahmed, Charles Collins — 2003

Related papers

• Piecewise Constant Signal Estimation by the Recording of Signal Measurements in a Linear SchemeН.Г. Михеев, A. I. Chulichkov, V. A. Antonyuk — 2021
• Noniterative interface reconstruction algorithms for volume of fluid methodT.G. Vignesh, Shamit Bakshi — 2013
• Calculation of reflection coefficient of complicated inhomogeneous layers using piecewise constant and piecewise linear approximationV. F. Borulko, O. O. Drobakhin, Д. В. Сидоров — 2011
• Error estimates for a discretized Galerkin method for a boundary integral equation in two dimensionsF. Penzel — 1992
• Piecewise linear double barrier optionsHangsuck Lee, Hongjun Ha, Minha Lee — 2021
• Manifold Piecewise Constant Systems and ChaosTadashi Tsubone, Toshimichi Saito — 1999
• Stability analysis of uncertain piecewise linear systems using Piecewise Quadratic Lyapunov FunctionsYuzo Ohta, Hisashi Yokoyama — 2010
• A New Piecewise Approach for Nonuniformity Correction in IRFPAYan Shi, Tianxu Zhang, Zhiguo Cao — 2004
• An accelerated hybrid Euler’s method for numerical integration of ordinary differential equationsTaimoor Zahro, Muhammad Anwar Solangi, Feroz Shah — 2020