We present a least-squares mixed finite element approximation of an elliptic problem with degenerate coefficients, arising in the study of the electronmagnetic field in a resonant structure with cylindrical symmetry. ...We present a least-squares mixed finite element approximation of an elliptic problem with degenerate coefficients, arising in the study of the electronmagnetic field in a resonant structure with cylindrical symmetry. Optimal error estimates are developed, especially in the case of differing polynomial degrees for the primary solution approximation uh and the flux approximation σh.展开更多
In this work we propose a numerical scheme for a nonlinear and degenerate parabolic problem having application in petroleum reservoir and groundwater aquifer simulation. The degeneracy of the equation includes both lo...In this work we propose a numerical scheme for a nonlinear and degenerate parabolic problem having application in petroleum reservoir and groundwater aquifer simulation. The degeneracy of the equation includes both locally fast and slow diffusion (i.e. the diffusion coefficients may explode or vanish in some point). The main difficulty is that the true solution is typically lacking in regularity. Our numerical approach includes a regularization step and a standard discretization procedure by means of C0-piecewise linear finite elements in space and backward-differences in time. Within this frame work, we analyze the accuracy of the scheme by using an integral test function and obtain several error estimates in suitable norms.展开更多
文摘We present a least-squares mixed finite element approximation of an elliptic problem with degenerate coefficients, arising in the study of the electronmagnetic field in a resonant structure with cylindrical symmetry. Optimal error estimates are developed, especially in the case of differing polynomial degrees for the primary solution approximation uh and the flux approximation σh.
文摘In this work we propose a numerical scheme for a nonlinear and degenerate parabolic problem having application in petroleum reservoir and groundwater aquifer simulation. The degeneracy of the equation includes both locally fast and slow diffusion (i.e. the diffusion coefficients may explode or vanish in some point). The main difficulty is that the true solution is typically lacking in regularity. Our numerical approach includes a regularization step and a standard discretization procedure by means of C0-piecewise linear finite elements in space and backward-differences in time. Within this frame work, we analyze the accuracy of the scheme by using an integral test function and obtain several error estimates in suitable norms.
