Numerical approximation of planar oblique derivative problems in nondivergence form
نویسندگان
چکیده
منابع مشابه
Verification and Validation of Common Derivative Terms Approximation in Meshfree Numerical Scheme
In order to improve the approximation of spatial derivatives without meshes, a set of meshfree numerical schemes for derivative terms is developed, which is compatible with the coordinates of Cartesian, cylindrical, and spherical. Based on the comparisons between numerical and theoretical solutions, errors and convergences are assessed by a posteriori method, which shows that the approximations...
متن کاملVariational Formulation and Numerical Analysis of Linear Elliptic Equations in Nondivergence form with Cordes Coefficients
This paper studies formulations of second-order elliptic partial differential equations in nondivergence form on convex domains as equivalent variational problems. The first formulation is that of Smears and Süli [SIAM J. Numer. Anal., 51 (2013), pp. 2088–2106], and the second one is a new symmetric formulation based on a least-squares functional. These formulations enable the use of standard f...
متن کاملNonuniqueness for some linear oblique derivative problems for elliptic equations
It is well-known that the “standard” oblique derivative problem, ∆u = 0 in Ω, ∂u/∂ν − u = 0 on ∂Ω (ν is the unit inner normal) has a unique solution even when the boundary condition is not assumed to hold on the entire boundary. When the boundary condition is modified to satisfy an obliqueness condition, the behavior at a single boundary point can change the uniqueness result. We give two simpl...
متن کاملDiscontinuous Galerkin Finite Element Approximation of Nondivergence Form Elliptic Equations with Cordès Coefficients
Abstract. Non-divergence form elliptic equations with discontinuous coefficients do not generally posses a weak formulation, thus presenting an obstacle to their numerical solution by classical finite element methods. We propose a new hp-version discontinuous Galerkin finite element method for a class of these problems that satisfy the Cordès condition. It is shown that the method exhibits a co...
متن کاملApproximation Schemes for Planar Graph Problems
Many NP-hard graph problems become easier to approximate on planar graphs and their generalizations. (A graph is planar if it can be drawn in the plane (or the sphere) without crossings. For definitions of other related graph classes, see the entry on Bidimensionality (2004; Demaine, Fomin, Hajiaghayi, Thilikos).) For example, maximum independent set asks to find a maximum subset of vertices in...
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: 2018
ISSN: 0025-5718,1088-6842
DOI: 10.1090/mcom/3371