Finite element methods for second order linear elliptic partial differential equations in non-divergence form

DOI10.1090/mcom/3168zbMath1364.65247arXiv1505.02842OpenAlexW2552708984MaRDI QIDQ2981768

Lauren Hennings, Xiaobing Feng, Michael Neilan

Publication date: 10 May 2017

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

Full work available at URL: https://arxiv.org/abs/1505.02842

zbMATH Keywords

convergencefinite element methodserror estimatenumerical experimentnon-divergence forminterior penalty termsecond-order linear elliptic partial differential equations

Mathematics Subject Classification ID

Boundary value problems for second-order elliptic equations (35J25) Error bounds for boundary value problems involving PDEs (65N15) 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)

Related Items (22)

Discontinuous Galerkin methods for a class of nonvariational problems ⋮ Recovery based finite difference scheme on unstructured mesh ⋮ A least square based weak Galerkin finite element method for second order elliptic equations in non-divergence form ⋮ Discrete ABP estimate and convergence rates for linear elliptic equations in non-divergence form ⋮ \(C^0\) finite element approximations of linear elliptic equations in non-divergence form and Hamilton-Jacobi-Bellman equations with Cordes coefficients ⋮ Convergence analysis of a finite element method for second order non-variational elliptic problems ⋮ Variational Formulation and Numerical Analysis of Linear Elliptic Equations in Nondivergence form with Cordes Coefficients ⋮ A C⁰ linear finite element method for a second‐order elliptic equation in non‐divergence form with Cordes coefficients ⋮ Error estimation for second‐order <scp>partial differential equations</scp> in nonvariational form ⋮ Numerical analysis of strongly nonlinear PDEs ⋮ A \(C^0\) finite element approximation of planar oblique derivative problems in non-divergence form ⋮ Discrete Miranda-Talenti estimates and applications to linear and nonlinear PDEs ⋮ Monotone meshfree methods for linear elliptic equations in non-divergence form via nonlocal relaxation ⋮ A primal-dual weak Galerkin finite element method for second order elliptic equations in non-divergence form ⋮ Finite element approximation of elliptic homogenization problems in nondivergence-form ⋮ Numerical approximation of planar oblique derivative problems in nondivergence form ⋮ Adaptive First-Order System Least-Squares Finite Element Methods for Second-Order Elliptic Equations in Nondivergence Form ⋮ Adaptive \(C^0\) interior penalty methods for Hamilton-Jacobi-Bellman equations with cordes coefficients ⋮ Mixed Finite Element Approximation of the Hamilton--Jacobi--Bellman Equation with Cordes Coefficients ⋮ Interior penalty discontinuous Galerkin methods for second order linear non-divergence form elliptic pdes ⋮ Ultraweak formulation of linear PDEs in nondivergence form and DPG approximation ⋮ A Sequential Least Squares Method for Elliptic Equations in Non-Divergence Form

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