A Modified Primal-Dual Weak Galerkin Finite Element Method for Second Order Elliptic Equations in Non-Divergence Form

zbMath1499.65683arXiv2011.11065MaRDI QIDQ5019882

Chunmei Wang

Publication date: 11 January 2022

Full work available at URL: https://arxiv.org/abs/2011.11065

zbMATH Keywords

finite element methodspolyhedral meshesweak Galerkinprimal-dualnon-divergence formCordès condition

Mathematics Subject Classification ID

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) Second-order elliptic equations (35J15) Strong solutions to PDEs (35D35)

Related Items

A primal-dual finite element method for transport equations in non-divergence form ⋮ A New Weak Galerkin Method with Weakly Enforced Dirichlet Boundary Condition ⋮ Curved elements in weak Galerkin finite element methods ⋮ Generalized weak Galerkin finite element methods for biharmonic equations

Cites Work

• An efficient numerical scheme for the biharmonic equation by weak Galerkin finite element methods on polygonal or polyhedral meshes
• Convergence analysis of a finite element method for second order non-variational elliptic problems
• Controlled Markov processes and viscosity solutions
• Discontinuous Galerkin Finite Element Approximation of Nondivergence Form Elliptic Equations with Cordès Coefficients
• 𝒞⁰ penalty methods for the fully nonlinear Monge-Ampère equation
• A weak Galerkin mixed finite element method for second order elliptic problems
• A primal-dual weak Galerkin finite element method for second order elliptic equations in non-divergence form