Boundary element monotone iteration scheme for semilinear elliptic partial differential equations
نویسندگان
چکیده
منابع مشابه
Boundary element monotone iteration scheme for semilinear elliptic partial differential equations
The monotone iteration scheme is a constructive method for solving a wide class of semilinear elliptic boundary value problems. With the availability of a supersolution and a subsolution, the iterates converge monotonically to one or two solutions of the nonlinear PDE. However, the rates of such monotone convergence cannot be determined in general. In addition, when the monotone iteration schem...
متن کاملBoundary Element Monotone Iteration Scheme for Semilinear Elliptic Partial Differential Equations, Part Ii: Quasimonotone Iteration for Coupled 2× 2 Systems
Numerical solutions of 2× 2 semilinear systems of elliptic boundary value problems, whose nonlinearities are of quasimonotone nondecreasing, quasimonotone nonincreasing, or mixed quasimonotone types, are computed. At each step of the (quasi) monotone iteration, the solution is represented by a simple-layer potential plus a domain integral; the simple-layer density is then discretized by boundar...
متن کاملBoundary element monotone iteration scheme for semilinear elliptic partial differential equations, Part II: Quasimonotone iteration for coupled systems
Numerical solutions of 2× 2 semilinear systems of elliptic boundary value problems, whose nonlinearities are of quasimonotone nondecreasing, quasimonotone nonincreasing, or mixed quasimonotone types, are computed. At each step of the (quasi) monotone iteration, the solution is represented by a simple-layer potential plus a domain integral; the simple-layer density is then discretized by boundar...
متن کاملFinite element methods for semilinear elliptic stochastic partial differential equations
We study finite element methods for semilinear stochastic partial differential equations. Error estimates are established. Numerical examples are also presented to examine our theoretical results. Mathematics Subject Classification (2000) 65N30 · 65N15 · 65C30 · 60H15
متن کاملThe Finite Element Approximation of Semilinear Elliptic Partial Differential Equations with Critical Exponents in the Cube
We consider the finite element solution of the parameterized semilinear elliptic equation ∆u + λu + u = 0, u > 0, where u is defined in the unit cube and is 0 on the boundary of the cube. This equation is important in analysis, and it is known that there is a value λ0 > 0 such that no solutions exist for λ < λ0. By solving a related linear equation we obtain an upper bound for λ0 which is also ...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Mathematics of Computation
سال: 1996
ISSN: 0025-5718
DOI: 10.1090/s0025-5718-96-00743-0