Quasi-norm error bounds for the finite element approximation of some degenerate quasilinear parabolic equations and variational inequalities

DOI10.1080/01630569508816675zbMath0861.65076OpenAlexW1998690850MaRDI QIDQ4883638

John W. Barrett, Wen-bin Liu

Publication date: 29 April 1997

Published in: Numerical Functional Analysis and Optimization (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1080/01630569508816675

zbMATH Keywords

variational inequalitiesSobolev spacefinite elementerror boundsregular solutiondegenerate quasilinear parabolic equationsbackward Euler time discretization

Mathematics Subject Classification ID

Numerical optimization and variational techniques (65K10) Variational inequalities (49J40) Nonlinear parabolic equations (35K55) Unilateral problems for linear parabolic equations and variational inequalities with linear parabolic operators (35K85) Degenerate parabolic equations (35K65) Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs (65M60) Error bounds for initial value and initial-boundary value problems involving PDEs (65M15)

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A Gradient Discretization Method to Analyze Numerical Schemes for Nonlinear Variational Inequalities, Application to the Seepage Problem ⋮ Weak Galerkin finite element method for a class of quasilinear elliptic problems ⋮ Error estimates and adaptive finite element methods ⋮ Galerkin infinite element approximation for pricing barrier options and options with discontinuous payoff ⋮ A theory of discretization for nonlinear evolution inequalities applied to parabolic Signorini problems ⋮ A posteriori error estimates for some model boundary control problems

Cites Work

• Unnamed Item
• A regularity theory for a general class of quasilinear elliptic partial differential equations and obstacle problems
• An \(L^ 2\)-error estimate for an approximation of the solution of a parabolic variational inequality
• Finite element error estimates for nonlinear elliptic equations of monotone type
• \(L^{\infty}\)-error estimate for an approximation of a parabolic variational inequality
• Error bounds for the finite element approximation of a degenerate quasilinear parabolic variational inequality
• SOME BOUNDARY-VALUE PROBLEMS FOR THE EQUATION 〈.(|〈φ|^N〈φ)=0
• Some qualitative properties of solutions of a generalised diffusion equation
• $L^\infty $-Convergence of Linear Finite Element Approximation to Nonlinear Parabolic Problems
• On the Obstacle Problem for Quasilinear Elliptic Equations of p Laplacian Type
• Existence, Uniqueness, and Numerical Analysis of Solutions of a Quasilinear Parabolic Problem
• A Convergence Estimate for an Approximation of a Parabolic Variational Inequality
• A further remark on the regularity of the solutions of the p-Laplacian and its applications to their finite element approximation
• Finite Element Approximation of the Parabolic p-Laplacian
• SIMILARITY SOLUTIONS IN SOME NON-LINEAR DIFFUSION PROBLEMS AND IN BOUNDARY-LAYER FLOW OF A PSEUDO-PLASTIC FLUID
• n-Diffusion

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