Positivity preserving finite element approximation

DOI10.1090/S0025-5718-01-01369-2zbMath1001.41011OpenAlexW2004898338MaRDI QIDQ3147167

Lars B. Wahlbin, Ricardo H. Nochetto

Publication date: 18 September 2002

Published in: Mathematics of Computation (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1090/s0025-5718-01-01369-2

zbMATH Keywords

finite elementsextreme pointspositive operatorssecond order accuracy

Mathematics Subject Classification ID

Error bounds for boundary value problems involving PDEs (65N15) Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs (65N30) Numerical interpolation (65D05) Rate of convergence, degree of approximation (41A25) Approximation by positive operators (41A36)

Related Items (17)

New formulations, positivity preserving discretizations and stability analysis for non-Newtonian flow models ⋮ An abstract framework for a priori estimates for contact problems in 3D with quadratic finite elements ⋮ Geometric Quasilinearization Framework for Analysis and Design of Bound-Preserving Schemes ⋮ Geometric transformation of finite element methods: theory and applications ⋮ A mixed finite element scheme for optimal control problems with pointwise state constraints ⋮ A finite element method for elliptic Dirichlet boundary control problems ⋮ Structure-Preserving Function Approximation via Convex Optimization ⋮ A posteriori error estimator competition for conforming obstacle problems ⋮ Global spatial regularity for elasticity models with cracks, contact and other nonsmooth constraints ⋮ Averaging techniques yield reliable a posteriori finite element error control for obstacle problems ⋮ Finite Element Approximation of the Parabolic Fractional Obstacle Problem ⋮ Variationally consistent discretization schemes and numerical algorithms for contact problems ⋮ Positivity preserving gradient approximation with linear finite elements ⋮ A sign preserving mixed finite element approximation for contact problems ⋮ A total variation diminishing interpolation operator and applications ⋮ Thermoviscoplasticity at small strains ⋮ Optimal Convergence for Discrete Variational Inequalities Modelling Signorini Contact in 2D and 3D without Additional Assumptions on the Unknown Contact Set

Cites Work

• Pointwise a posteriori error control for elliptic obstacle problems
• Residual type a posteriori error estimates for elliptic obstacle problems
• Approximation in the finite element method
• Finite Element Interpolation of Nonsmooth Functions Satisfying Boundary Conditions
• Mixed and Hybrid Finite Element Methods
• A Mollifier Useful for Approximations in Sobolev Spaces and Some Applications to Approximating Solutions of Differential Equations
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