A priori and a posteriori error analysis for semilinear problems in liquid crystals
DOI10.1051/m2an/2023056OpenAlexW4381050752MaRDI QIDQ6181258
Apala Majumdar, Neela Nataraj, Ruma Rani Maity
Publication date: 22 January 2024
Published in: ESAIM: Mathematical Modelling and Numerical Analysis (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1051/m2an/2023056
nematic liquid crystalserror analysisnon-homogeneous Dirichlet boundary conditionsNitsche's methodnon-linear elliptic PDEsferronematicsconforming FEMa priori and a posterioridiscontinuous Galerkin and WOPSIP methods
Smoothness and regularity of solutions to PDEs (35B65) PDEs in connection with fluid mechanics (35Q35) Error bounds for boundary value problems involving PDEs (65N15) Nonlinear elliptic equations (35J60) Stability and convergence of numerical methods for boundary value problems involving PDEs (65N12) Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs (65N30) Statistical mechanics of random media, disordered materials (including liquid crystals and spin glasses) (82D30) A priori estimates in context of PDEs (35B45) Second-order elliptic equations (35J15) Liquid crystals (76A15) Finite element methods applied to problems in fluid mechanics (76M10) Biharmonic, polyharmonic functions and equations, Poisson's equation in two dimensions (31A30)
Cites Work
- Quasi-optimal convergence rate of an adaptive weakly over-penalized interior penalty method
- A posteriori error control for a weakly over-penalized symmetric interior penalty method
- Parameter dependent finite element analysis for ferronematics solutions
- A weakly over-penalized symmetric interior penalty method
- Quasi-optimal and pressure robust discretizations of the Stokes equations by moment- and divergence-preserving operators
- Error analysis of Nitsche's and discontinuous Galerkin methods of a reduced Landau-de Gennes problem
- Über ein Variationsprinzip zur Lösung von Dirichlet-Problemen bei Verwendung von Teilräumen, die keinen Randbedingungen unterworfen sind. (On a variational principle for solving Dirichlet problems less boundary conditions using subspaces)
- Nitsche’s method for general boundary conditions
- A new error analysis for discontinuous finite element methods for linear elliptic problems
- A posteriori error analysis for locally conservative mixed methods
- Finite Element Interpolation of Nonsmooth Functions Satisfying Boundary Conditions
- Equilibrium order parameters of nematic liquid crystals in the Landau-de Gennes theory
- Conforming and nonconforming finite element methods for solving the stationary Stokes equations I
- A Posteriori Error Estimates for a Discontinuous Galerkin Approximation of Second-Order Elliptic Problems
- Nonconforming finite element discretization for semilinear problems with trilinear nonlinearity
- Lowest-order equivalent nonstandard finite element methods for biharmonic plates
- Discontinuous Galerkin finite element methods for the Landau–de Gennes minimization problem of liquid crystals
- The completion of locally refined simplicial partitions created by bisection
- The Mathematical Theory of Finite Element Methods
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- Unnamed Item
- Unnamed Item
- Unnamed Item
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