A C0 linear finite element method for a second‐order elliptic equation in non‐divergence form with Cordes coefficients

DOI10.1002/num.22965arXiv2211.04037MaRDI QIDQ6086368

Min-Qiang Xu, Runchang Lin, Qingsong Zou

Publication date: 12 December 2023

Published in: Numerical Methods for Partial Differential Equations (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2211.04037

zbMATH Keywords

discontinuous coefficientssuperconvergencegradient recoveryMonge-Ampère equationsnon-divergence formCordes conditionlinear finite elementHessian recovery

Mathematics Subject Classification ID

Numerical analysis (65-XX) Partial differential equations (35-XX)

Related Items (1)

A REPRODUCING KERNEL METHOD FOR SOLVING SINGULARLY PERTURBED DELAY PARABOLIC PARTIAL DIFFERENTIAL EQUATIONS

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Polynomial preserving recovery on boundary
• Vanishing moment method and moment solutions for fully nonlinear second order partial differential equations
• Über die erste Randwertaufgabe bei quasilinearen Differentialgleichungen zweiter Ordnung in mehr als zwei Variablen
• Numerical solution of the two-dimensional elliptic Monge--Ampère equation with Dirichlet boundary conditions: An augmented Lagrangian approach
• Discrete ABP estimate and convergence rates for linear elliptic equations in non-divergence form
• Polynomial preserving recovery for high frequency wave propagation
• A \(C^0\) linear finite element method for biharmonic problems
• Interior penalty discontinuous Galerkin methods for second order linear non-divergence form elliptic pdes
• Numerical solution of the Monge--Ampère equation by a Newton's algorithm
• Monotone mixed finite difference scheme for Monge-Ampère equation
• Quadratic finite element approximations of the Monge-Ampère equation
• An efficient method based on least-squares technique for interface problems
• A least square based weak Galerkin finite element method for second order elliptic equations in non-divergence form
• Hessian recovery based finite element methods for the Cahn-Hilliard equation
• Adaptive \(C^0\) interior penalty methods for Hamilton-Jacobi-Bellman equations with cordes coefficients
• A fourth-order least-squares based reproducing kernel method for one-dimensional elliptic interface problems
• Finite element methods for fully nonlinear second order PDEs based on a discrete Hessian with applications to the Monge-Ampère equation
• The polynomial-preserving recovery for higher order finite element methods in 2D and 3D
• Controlled Markov processes and viscosity solutions
• Discontinuous Galerkin Finite Element Approximation of Nondivergence Form Elliptic Equations with Cordès Coefficients
• A Finite Element Method for Nonlinear Elliptic Problems
• Hessian recovery for finite element methods
• Finite element methods for second order linear elliptic partial differential equations in non-divergence form
• 𝒞⁰ penalty methods for the fully nonlinear Monge-Ampère equation
• A Finite Element Method for Second Order Nonvariational Elliptic Problems
• Convergent Finite Difference Solvers for Viscosity Solutions of the Elliptic Monge–Ampère Equation in Dimensions Two and Higher
• Two Numerical Methods for the elliptic Monge-Ampère equation
• Some A Posteriori Error Estimators for Elliptic Partial Differential Equations
• The superconvergent patch recovery anda posteriori error estimates. Part 1: The recovery technique
• Maxwell and Lamé eigenvalues on polyhedra
• Asymptotically Exact A Posteriori Error Estimators, Part I: Grids with Superconvergence
• A primal-dual weak Galerkin finite element method for second order elliptic equations in non-divergence form
• A Discontinuous Galerkin Finite Element Method fOR Uniformly Elliptic Two Dimensional Oblique Boundary-Value Problems
• Convergent Filtered Schemes for the Monge--Ampère Partial Differential Equation
• A DGFEM for nondivergence form elliptic equations with Cordes coefficients on curved domains
• A New Finite Element Gradient Recovery Method: Superconvergence Property
• Variational Formulation and Numerical Analysis of Linear Elliptic Equations in Nondivergence form with Cordes Coefficients
• Discontinuous Galerkin Finite Element Approximation of Hamilton--Jacobi--Bellman Equations with Cordes Coefficients
• Error estimation for second‐order <scp>partial differential equations</scp> in nonvariational form

This page was built for publication: A C⁰ linear finite element method for a second‐order elliptic equation in non‐divergence form with Cordes coefficients