Abstract
An optimally convergent (with respect to the regularity) quadratic finite element method for the two-dimensional obstacle problem on simplicial meshes is studied in [14]. There was no analogue of a quadratic finite element method on tetrahedron meshes for the three-dimensional obstacle problem. In this article, a quadratic finite element enriched with element-wise bubble functions is proposed for the three-dimensional elliptic obstacle problem. A priori error estimates are derived to show the optimal convergence of the method with respect to the regularity. Further, a posteriori error estimates are derived to design an adaptive mesh refinement algorithm. A numerical experiment illustrating the theoretical result on a priori error estimates is presented.
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© 2018 Walter de Gruyter GmbH, Berlin/Boston
Articles in the same Issue
- Frontmatter
- A Two-Level Sparse Grid Collocation Method for Semilinear Stochastic Elliptic Equation
- A Study on the Galerkin Least-Squares Method for the Oldroyd-B Model
- A Short Note on the Connection Between Layer-Adapted Exponentially Graded and S-Type Meshes
- GMRES Convergence Bounds for Eigenvalue Problems
- Bubbles Enriched Quadratic Finite Element Method for the 3D-Elliptic Obstacle Problem
- Spectral Analysis, Properties and Nonsingular Preconditioners for Singular Saddle Point Problems
- Domain Decomposition Methods for Recovering Robin Coefficients in Elliptic and Parabolic Systems
- Semi-Discrete Galerkin Finite Element Method for the Diffusive Peterlin Viscoelastic Model
- Optimal Strong Rates of Convergence for a Space-Time Discretization of the Stochastic Allen–Cahn Equation with Multiplicative Noise
- Modified Minimal Error Method for Nonlinear Ill-Posed Problems
Articles in the same Issue
- Frontmatter
- A Two-Level Sparse Grid Collocation Method for Semilinear Stochastic Elliptic Equation
- A Study on the Galerkin Least-Squares Method for the Oldroyd-B Model
- A Short Note on the Connection Between Layer-Adapted Exponentially Graded and S-Type Meshes
- GMRES Convergence Bounds for Eigenvalue Problems
- Bubbles Enriched Quadratic Finite Element Method for the 3D-Elliptic Obstacle Problem
- Spectral Analysis, Properties and Nonsingular Preconditioners for Singular Saddle Point Problems
- Domain Decomposition Methods for Recovering Robin Coefficients in Elliptic and Parabolic Systems
- Semi-Discrete Galerkin Finite Element Method for the Diffusive Peterlin Viscoelastic Model
- Optimal Strong Rates of Convergence for a Space-Time Discretization of the Stochastic Allen–Cahn Equation with Multiplicative Noise
- Modified Minimal Error Method for Nonlinear Ill-Posed Problems