A Galerkin Method for a Nonlinear Dirichlet Problem
Copyright policy )A Galerkin Method for a Nonlinear Dirichlet Problem
A Galerkin method due to Nitsche for treating the Dirichlet problem for a linear second-order elliptic equation is extended to cover the nonlinear equation ∇ ⋅ ( a ( x , u ) ∇ u ) = f \nabla \cdot (a(x,u)\nabla u) = f . The asymptotic error estimates are of the same form as in the linear case. Newton’s method can be used to solve the nonlinear algebraic equations.
Boundary value problems for second-order elliptic equations, Error bounds for boundary value problems involving PDEs, Numerical computation of solutions to systems of equations, Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs, Nonlinear elliptic equations
Boundary value problems for second-order elliptic equations, Error bounds for boundary value problems involving PDEs, Numerical computation of solutions to systems of equations, Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs, Nonlinear elliptic equations
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