Inhaltszusammenfassung

We propose a least squares formulation for the numerical approximation of parabolic partial differential equations, which minimizes the residual of the equation using the natural norm. In particular, we avoid making regularity assumptions on the problem's data. The resulting bilinear form is symmetric, continuous, and coercive in this approach. This paves the way for Galerkin frameworks for the numerical approximation of solutions to parabolic equations. In this work, we restrict ourselves t...We propose a least squares formulation for the numerical approximation of parabolic partial differential equations, which minimizes the residual of the equation using the natural norm. In particular, we avoid making regularity assumptions on the problem's data. The resulting bilinear form is symmetric, continuous, and coercive in this approach. This paves the way for Galerkin frameworks for the numerical approximation of solutions to parabolic equations. In this work, we restrict ourselves to one spatial dimension. Negative Sobolev norms appearing in the formulation are evaluated analytically within the numerical approach.» weiterlesen» einklappen

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