Global C...-regularity for second order quasilinear elliptic euqations in divergence form.
Global inverse problem of the Sturm-Liouville type for a linear elliptic partial differential equation of second order
Global Lipschitz continuity for elliptic transmission problems with a boundary intersecting interface
We investigate the regularity of the weak solution to elliptic transmission problems that involve two layered anisotropic materials separated by a boundary intersecting interface. Under a pair of compatibility conditions for the angle of the two surfaces and the boundary data at the contact line, we prove the existence of up to the boundary square-integrable second derivatives, and the global Lipschitz continuity of the solution. If only the weakest, necessary condition is satisfied, we show that...
Global regularity of the solutions to the capillarity problem
Gravimetric quasigeoid in Slovakia by the finite element method
The paper presents the solution to the geodetic boundary value problem by the finite element method in area of Slovak Republic. Generally, we have made two numerical experiments. In the first one, Neumann BC in the form of gravity disturbances generated from EGM-96 is used and the solution is verified by the quasigeoidal heights generated directly from EGM-96. In the second one, Neumann BC is computed from gravity measurements and the solution is compared to the quasigeoidal heights obtained by...
Growth rate and existence of solutions to Dirichlet problems for prescribed mean curvature equations on unbounded domains.
Guaranteed and robust a posteriori error estimates for singularly perturbed reaction–diffusion problems
We derive a posteriori error estimates for singularly perturbed reaction–diffusion problems which yield a guaranteed upper bound on the discretization error and are fully and easily computable. Moreover, they are also locally efficient and robust in the sense that they represent local lower bounds for the actual error, up to a generic constant independent in particular of the reaction coefficient. We present our results in the framework of the vertex-centered finite volume method but their nature...
convergence of solutions of a biharmonic problem on a truncated convex sector near the angle
We consider a biharmonic problem with Navier type boundary conditions , on a family of truncated sectors in of radius , and opening angle , when is close to . The family of right-hand sides is assumed to depend smoothly on in . The main result is that converges to when with respect to the -norm. We can also show that the -topology is optimal for such a convergence result.
-finite element approximations on non-matching grids for partial differential equations with non-negative characteristic form
We propose and analyze a domain decomposition method on non-matching grids for partial differential equations with non-negative characteristic form. No weak or strong continuity of the finite element functions, their normal derivatives, or linear combinations of the two is imposed across the boundaries of the subdomains. Instead, we employ suitable bilinear forms defined on the common interfaces, typical of discontinuous Galerkin approximations. We prove an error bound which is optimal with respect...
Hardy inequalities with boundary terms.
Harmonic averages, exact difference schemes and local Green’s functions in variable coefficient PDE problems
A brief survey is given to show that harmonic averages enter in a natural way in the numerical solution of various variable coefficient problems, such as in elliptic and transport equations, also of singular perturbation types. Local Green’s functions used as test functions in the Petrov-Galerkin finite element method combined with harmonic averages can be very efficient and are related to exact difference schemes.
Harmonic functions satisfying weighted sign conditions on the boundary
Hexahedral H(div) and H(curl) finite elements
We study the approximation properties of some finite element subspaces of H(div;Ω) and H(curl;Ω) defined on hexahedral meshes in three dimensions. This work extends results previously obtained for quadrilateral H(div;Ω) finite elements and for quadrilateral scalar finite element spaces. The finite element spaces we consider are constructed starting from a given finite dimensional space of vector fields on the reference cube, which is then transformed to a space of vector fields on a hexahedron using...
Hexahedral H(div) and H(curl) finite elements*
We study the approximation properties of some finite element subspaces of H(div;Ω) and H(curl;Ω) defined on hexahedral meshes in three dimensions. This work extends results previously obtained for quadrilateral H(div;Ω) finite elements and for quadrilateral scalar finite element spaces. The finite element spaces we consider are constructed starting from a given finite dimensional space of vector fields on the reference cube, which is then transformed to a space of vector fields on a hexahedron...
High frequency asymptotic solutions of the reduced wave equation on infinite regions with nonconvex boundaries.
High order transmission conditions for thin conductive sheets in magneto-quasistatics
We propose transmission conditions of order 1, 2 and 3 approximating the shielding behaviour of thin conducting curved sheets for the magneto-quasistatic eddy current model in 2D. This model reduction applies to sheets whose thicknesses ε are at the order of the skin depth or essentially smaller. The sheet has itself not to be resolved, only its midline is represented by an interface. The computation is directly in one step with almost no additional cost. We prove the well-posedness w.r.t. to...
High order transmission conditions for thin conductive sheets in magneto-quasistatics
We propose transmission conditions of order 1, 2 and 3 approximating the shielding behaviour of thin conducting curved sheets for the magneto-quasistatic eddy current model in 2D. This model reduction applies to sheets whose thicknesses ε are at the order of the skin depth or essentially smaller. The sheet has itself not to be resolved, only its midline is represented by an interface. The computation is directly in one step with almost no additional cost. We prove the well-posedness w.r.t. to...
Higher asymptotics of the complex Monge-Ampère equation
High-order finite difference schemes and Toeplitz based preconditioners for elliptic problems.
Hitting probabilities and potential theory for the brownian path-valued process
We consider the Brownian path-valued process studied in [LG1], [LG2], which is closely related to super Brownian motion. We obtain several potential-theoretic results related to this process. In particular, we give an explicit description of the capacitary distribution of certain subsets of the path space, such as the set of paths that hit a given closed set. These capacitary distributions are characterized as the laws of solutions of certain stochastic differential equations. They solve variational...